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Worksheets

Unit 1A review

Total questions: 135

Worksheet time: 5hrs 1mins

Name
Class
Date
1.

_________________ is the process of reaching a conclusion based on a pattern of examples.

a)

conjecture

b)

deductive reasoning

c)

inductive reasoning

d)

counterexample

2.

A ____________ is an educated guess.

a)

conjecture

b)

conclusion

c)

conjunction

d)

counterexample

3.

A ______________ is a number, drawing, or a statement that proves a conjecture to be false.

a)

conflation

b)

counterexample

c)

confluence

d)

conclusion

4.

A __________________ is a compound statement that consists of a hypothesis and conclusion.

"If p then q"

a)

contrapositive

b)

converse

c)

inverse

d)

conditional statement

5.

A ____________ is the part of the conditional statement that follows the word "if"

a)

hypothesis

b)

converse

c)

conclusion

d)

inverse

6.

A ____________ is the part of the conditional statement that follows the word "then"

a)

hypothesis

b)

converse

c)

conclusion

d)

inverse

7.

A ____________ is formed by exchanging the hypothesis and conclusion of the conditional.

"if q then p"

a)

counterexample

b)

contrapositive

c)

inverse

d)

converse

8.

A ____________ is formed by negating the hypothesis and conclusion of the conditional.

"if ~p then ~q"

a)

counterexample

b)

contrapositive

c)

inverse

d)

converse

9.

A ____________ is formed by exchanging AND negating the hypothesis and conclusion of the conditional.

"if ~q then ~p"

a)

counterexample

b)

contrapositive

c)

inverse

d)

converse

10.

Given:

If the phone is ringing, then someone is calling.


Identify the hypothesis (p) and conclusion (q).

a)

p: someone is calling

q: the phone is ringing

b)

p: the phone is ringing

q: someone is calling

c)

p: the phone is not ringing

q: someone is not calling

d)

p: someone is not calling

q: the phone is not ringing

11.

Given:

If the phone is ringing, then someone is calling.


Write the converse.

a)

If someone is calling then the phone is ringing

b)

If the phone is ringing then someone is calling

c)

If the phone is not ringing then someone is not calling

d)

If someone is not calling then the phone is not ringing

12.

Given:

If the phone is ringing, then someone is calling.


Write the inverse.

a)

If someone is calling then the phone is ringing

b)

If the phone is ringing then someone is calling

c)

If the phone is not ringing then someone is not calling

d)

If someone is not calling then the phone is not ringing

13.

Given:

If the phone is ringing, then someone is calling.


Write the contrapositive.

a)

If someone is calling then the phone is ringing

b)

If the phone is ringing then someone is calling

c)

If the phone is not ringing then someone is not calling

d)

If someone is not calling then the phone is not ringing

14.

Which two statements are logically equivalent ?

(more than one answer)

a)

conditional and converse

b)

inverse and contrapositive

c)

conditional and inverse

d)

conditional and contrapositive

e)

converse and inverse

15.

A ____________ is the linking a conditional and its converse with the words "if an only if".

a)

biconditional

b)

extraconditional

c)

aerconditional

d)

intraconditional

16.

Given:

If Jack ran the fastest mile, then he won first prize.


Write the biconditional for the statement.

a)

Jack won first prize if and only if he didn't win first prize.

b)

Jack ran the fastest mile if and only if he won first prize

c)

Jack didn't win the fastest mile if and only if he didn't win first prize.

d)

Jack won first prize if and only if he didn't run the fastest mile.

17.
Step 2 is what
a)
Substitution property (simplify)
b)
Multiplication property of equality
c)
Division property of equality
d)
Distributive Property
18.
What is always the 1st statement in reason column of a proof?
a)
Prove
b)
Given
c)
Reason
d)
Statement
19.
Identify the property used here:
39=39
a)
Reflexive
b)
Symmetric
c)
Transitive
d)
Substitution
20.
What is step 4
a)
Substitution property (simplify)
b)
Addition property of equality
c)
Subtraction property of equality
21.
What is reason 2?
a)
Addition Property of Equality
b)
Subtraction Property of Equality
c)
Multiplication Property of Equality
d)
Division Property of Equality
22.
Identify the property of equality.
If 9=x, then x=9
a)
Reflexive
b)
Symmetric
c)
Transitive
d)
Substitution
23.
What is reason 1?
a)
Subtraction Property of Equality
b)
Transitive Property of Equality
c)
Given
d)
Prove
24.
What is reason 1?
a)
Subtraction Property of Equality
b)
Transitive Property of Equality
c)
Given
d)
Prove
25.
What is reason 2?
a)
Given
b)
Addition Property of Equality
c)
Subtraction Property of Equality
d)
Substitution Property of Equality
26.
What is reason 3?
a)
Addition Property of Equality
b)
Subtraction Property of Equality
c)
Multiplication Property of Equality
d)
Division Property of Equality
27.

What is the fifth Reason?

a)

Symmetric Property of Equality

b)

Subtraction Property of Equality

c)

Multiplication Property of Equality

d)

Division Property of Equality

28.

Name the Property that this statement illustrates:

If x = y, then 3x = 3y.

a)

Multiplication Property Of Equality

b)

Addition Property Of Equality

c)

Symmetric Property Of Equality

29.

Name the property that this statement illustrates:

If g = h, then h = g.

a)

Symmetric Property Of Equality

b)

Subtraction Property Of Equality

30.
Identify the property of equality.
If 9=x, then x=9
a)
Reflexive
b)
Symmetric
c)
Transitive
d)
Substitution
31.
What is Addition property of equality
a)
a.   If a=b, then a+c=b+c
b)
b.  If a=b, then a-c=b-c
c)
c.  If a=b, then ac=bc
d)
d.  If a=b, then a/c=b/c
32.
Identify the property used here:
39=39
a)
Reflexive
b)
Symmetric
c)
Transitive
d)
Substitution
33.
Simplify the expression with the distributive property
6(x + 3)
a)
6x + 3
b)
6x + 18
c)
x + 3
d)
9x
34.

What is usually the 1st statement in reason column of a proof?

a)

Prove

b)

Given

c)

Reason

d)

Statement

35.
Step 2 is what
a)
Substitution property (simplify)
b)
Multiplication property of equality
c)
Division property of equality
d)
Distributive Property
36.
Step 1 is what
a)
addition property of equality
b)
given
c)
subtraction property of equality
d)
prove
37.
What is reason 2?
a)
Addition Property of Equality
b)
Subtraction Property of Equality
c)
Multiplication Property of Equality
d)
Division Property of Equality
38.
For any numbers a, b, and c, if a = b and b = c, then a = c.
a)
Transitive Property         
b)
Symmetric Property
c)
Reflexive Property
d)
Substitution Property
39.
What is reason 1?
a)
Subtraction Property of Equality
b)
Transitive Property of Equality
c)
Given
d)
Prove
40.
What is step 6
a)
Subtraction property of equality
b)
Addition property of equality
c)
Division property of equality
41.
What is reason 5?
a)
Transitive Property
b)
Reflexive Property
c)
Symmetric Property
d)
Prove
42.
What is reason 3?
a)
Addition Property of Equality
b)
Subtraction Property of Equality
c)
Multiplication Property of Equality
d)
Division Property of Equality
43.
What is reason 4?
a)
Addition Property of Equality
b)
Subtraction Property of Equality
c)
Multiplication Property of Equality
d)
Division Property of Equality
44.

Which of the following is true about the conditional statement below?

If a man is 7 feet tall, then he plays basketball.

a)

Hypothesis: a man is 7 feet tall

Conclusion: he plays basketball

b)

Hypothesis: IF a man is 7 feet tall

Conclusion: THEN he plays basketball

c)

Hypothesis: THEN he plays basketball

Conclusion: IF a man is 7 feet tall

d)

Hypothesis: he plays basketball

Conclusion: a man is 7 feet tall

45.

Which of the following is true about the conditional statement below?

If you are flying, then you are in a

jet.

a)

Hypothesis: you are flying

Conclusion: you are in a

jet

b)

Hypothesis: IF you are flying

Conclusion: THEN you are in a

jet

c)

Hypothesis: THEN you are in a

jet

Conclusion: IF you are flying

d)

Hypothesis: you are in a

jet

Conclusion: you are flying

46.

Which of the following is true about the conditional statement below?

If you are in Alaska, then you are

cold.

a)

Hypothesis: you are in Alaska

Conclusion: you are

cold

b)

Hypothesis: IF you are in Alaska

Conclusion: THEN you are

cold

c)

Hypothesis: THEN you are

cold

Conclusion: IF you are in Alaska

d)

Hypothesis: you are

cold

Conclusion: you are in Alaska

47.

Which of the following is the CONVERSE of the statement below?

If an object is a ring, then it is

made of gold.

a)

If an object is made of gold, then it is a ring.

b)

If an object is not a ring, then it is not made of god.

c)

If an object is not made of gold, then it is not a ring.

d)

There is no converse of the statement.

48.

Which of the following is the CONVERSE of the statement below?

If an object is a bird, then it can fly.

a)

If an object can fly, then it is a bird.

b)

If an object is not a bird, then it cannot fly

c)

If an object cannot fly, then it is not a bird

d)

There is no converse of the statement

49.

Which of the following is the CONVERSE of the statement below?

If your grade is a 96, then you are

making an A.

a)

If you are making an A, then your grade is a 96.

b)

If you are not making an A, then your grade is not a 96.

c)

If your grade is not a 96, then you are not making an A.

d)

There is no converse of the statement.

50.

Which of the following is the CONVERSE of the statement below?

If you play football, then you wear

a uniform.

a)

If you wear a uniform, then you play football.

b)

If you do not play football, then you do not wear a uniform.

c)

If you do not wear a uniform, then you do not play football.

d)

There is no converse of the statement.

51.

Which of the following is the INVERSE of the statement below?

If an object is a computer, then it

has a hard drive.

a)

If an object is not a computer, then it does not have a hard drive.

b)

If an object does not have a hard drive, then it is not a computer.

c)

If an object has a hard drive, then it is a computer.

d)

There is no inverse of the statement.

52.

Which of the following is the INVERSE of the statement below?

If an object is a battery, then it is

rechargeable.

a)

If an object is not a battery, then it is not

rechargeable.

b)

If an object is rechargeable, then it is not a battery.

c)

If an object is not rechargeable, then it is not a battery.

d)

There is no inverse of the statement.

53.

Which of the following is the INVERSE of the statement below?

If an animal is black and white,

then it is a penguin.

a)

If an animal is not black and white, then it is not a penguin

b)

If an animal is a penguin, then it is black and white.

c)

If an animal is not a penguin, then it is not black and white.

d)

There is no inverse of the statement.

54.

Which of the following is the CONTRAPOSITIVE of the statement below?

If a species walks on two feet, then

it is human.

a)

If a species is not human, then it does not walk on two feet.

b)

If a species is human, then it walks on two feet.

c)

If a species does not walk on two feet, then it is not human.

d)

There is no contrapositive of the statement.

55.

Which of the following is the CONTRAPOSITIVE of the statement below?

If a gem is a ruby, then it is red.

a)

If a gem is not red, then it is not a ruby.

b)

If a gem is not a ruby, then it is not red.

c)

If a gem is red, then it is a ruby.

d)

There is no contrapositive statement.

56.

Which of the following is the CONTRAPOSITIVE of the statement below?

If a species is a fish, then it lives in

water.

a)

If a species does not live in water, then it is not a fish.

b)

If a species is not a fish, then it does not live in water.

c)

If a species lives in water, then it is a fish.

d)

There is not contrapositive of the statement.

57.

Which of the following is the BICONDITIONAL of the statement below?

If there is lightning, then there is thunder.

a)

If there is not lightning, then there is not thunder.

b)

If there is thunder, then there is lightning.

c)

There is lightning if and only if (iff) there is thunder.

d)

There is no biconditional statement.

58.

Which of the following is the BICONDITIONAL of the statement below?

If it is water, then it is wet.

a)

If it is not wet, then it is not water.

b)

If it is wet, then it is water.

c)

It is water if and only if (iff) it is wet.

d)

There is no biconditional statement.

59.

Which of the following is a valid conditional statement for the following phrase:

An acute angle has a measure less than 90°.

a)

If an angle is acute, then it has a measure less than 90°.

b)

If an angle is not acute, then it does not have a measure less than 90°.

c)

If an angle is acute, then it is acute.

d)

If an angle does not measure less than 90°, then it is not acute.

60.

If the conditional statement was "If an angle is acute, then it has a measure less than 90°.", which type of statement is the following?

An angle is acute if and only if (iff) it has a measure less than 90°.

a)

Biconditional

b)

Converse

c)

Inverse

d)

Contrapositive

61.

If the conditional statement was "If an angle is acute, then it has a measure less than 90°.", which type of statement is the following?

If an angle does not have a measure less than 90°, then it is not acute.

a)

Contrapositive

b)

Converse

c)

Biconditional

d)

Inverse

62.

If the conditional statement was "If an angle is acute, then it has a measure less than 90°.", which type of statement is the following?

If an angle has a measure less than 90°, then it is acute.

a)

Converse

b)

Contrapositive

c)

Biconditional

d)

Inverse

63.

If the conditional statement was "If an angle is acute, then it has a measure less than 90°.", which type of statement is the following?

If an angle is not acute, then it does not have a measure less than 90°.

a)

Inverse

b)

Contrapositive

c)

Biconditional

d)

Converse

64.
This is what kind of angle?
a)
obtuse
b)
right
c)
straight
d)
acute
65.
Name this angle.
a)
acute
b)
right
c)
obtuse
d)
none of the above
66.
Name this angle.
a)
acute
b)
right
c)
obtuse
d)
none of the above
67.
Another name for a right angle is ___________.
a)
square angle
b)
correct angle
c)
90 degree angle
d)
none of the above
68.

Find the missing angle.

a)

43

b)

47

c)

57

d)

67

69.
a)
x = 118
b)
x = 108
c)
x = 28
d)
x = 58
70.
How are these angles related?
a)
Vertrical
b)
Complementary 
c)
Adjacent
d)
Supplementary 
71.
what kind of angle is this? 
a)
straight
b)
acute
c)
obtuse
d)
right
72.
Part of a line. Has two endpoints and includes all of the points in between.
a)
Point
b)
Angle
c)
Line
d)
Line Segment
73.
A__________ is a fixed position in space and has no dimensions or size.
a)
Point
b)
Line
c)
Plane
d)
Cube
74.
Name the image
a)
Line
b)
Ray
c)
Line segment
d)
Angle
75.
Name the Image
a)
Angle
b)
Line
c)
Line Segment
d)
Ray
76.
Points that lie on the same line are _________.
a)
coplanar
b)
collinear
c)
parallel
d)
perpendicular
77.
A line is named by...
a)
Any 2 points on the line, or a lowercase script letter.
b)
Any 3 points on the line.
c)
Any 1 point on the line.
d)
Any 3 points on the line, or a uppercase script letter.
78.
A plane is named by...
a)
Any 1 point on the plane.
b)
Any 3 collinear points on the plane or a lowercase script letter.
c)
Any 3 non-collinear points on the plane or an uppercase script letter.
d)
All points on the plane that aren't part of a line.
79.
An angle is made up of two _____________ that share a common ________________. 
a)
rays, endpoint
b)
endpoint, rays
c)
vertexes, name
d)
angles, point
80.
What are complementary angles?
a)
Angles that add up to 180°
b)
Angles that add up to 90°
c)
Angles that are equal to each other
d)
Angles that are opposite of each other when lines intersect.
81.

Choose the correct name for the angle marked ∠3.\angle3.  

a)

∠V\angle V  

b)

∠4\angle4  

c)

∠IVH\angle IVH  

d)

∠JVI\angle JVI  

82.

Name the vertex of the angle.

a)

E

b)

F

c)

D

d)

E, F, and D are vertices

83.
What does the image show?
a)
a line
b)
a line segment
c)
a ray
d)
a point
84.
Write the following statement in if-then form.
All students at Hermitage take an English class.
a)
If you take an English class, then you are a student at Hermitage.
b)
If you are a student at Hermitage, then you take an English. class
85.
What is the converse of the following statement?
If it is Saturday, then the school is closed
a)
If the school is closed, then it is Saturday.
b)
If it is not Saturday, then the school is not closed.
c)
If the school is not closed, then it is not Saturday.
86.
What is the inverse of the following statement?
If it is Saturday, then the school is closed
a)
If the school is closed, then it is Saturday.
b)
If it is not Saturday, then the school is not closed.
c)
If the school is not closed, then it is not Saturday.
87.
What is the contrapositive of the following statement?
If it is Saturday, then the school is closed
a)
If the school is closed, then it is Saturday.
b)
If it is not Saturday, then the school is not closed.
c)
If the school is not closed, then it is not Saturday.
88.
Let p represent "Daniel is angry", and let q represent "Daniel is not having fun."
Translate the following symbolic form into written form... 
      p ^ ~ q
a)
Daniel is not having fun and Daniel is angry.
b)
Daniel is having fun and Daniel is not angry.
c)
Daniel is angry and Daniel is having fun. 
d)
Daniel is angry and Daniel is not having fun.
89.
Let p represent "Daniel is angry", and let q represent "Daniel is not having fun."
Translate the following symbolic form into written form... 
      ~ q ^ p
a)
Daniel is not having fun and Daniel is angry.
b)
Daniel is having fun and Daniel is angry.
c)
Daniel is angry and Daniel is having fun. 
d)
Daniel is angry and Daniel is not having fun.
90.
Conditional: If it does not rain today, then we will have practice.
What is this statement called: If it rains today, then we will not have practice.
a)
Converse
b)
Inverse
c)
Contrapositive
d)
Negation
91.
What does this mean?
a)
Conditional Statement
b)
Inverse
c)
Converse
d)
THIS IS A GEOMETRY CLASS!!! GIVE ME NUMBERS!
92.
What does this mean?
a)
Conditional Statement
b)
Inverse Statement
c)
Converse Statement
d)
Contrapositive Statement
93.
What does this mean?
a)
Conditional Statement
b)
Converse
c)
Inverse
d)
Contrapositive
94.
What is the conclusion to the statement?
a)
You like fried chicken
b)
You only like fried chicken from KFC
c)
You like KFC
d)
You hate KFC
95.
What is the hypothesis of this conditional?
a)
Sally goes to the park.
b)
Sally will fall off the swing.
c)
Parks don't have swings that Sally goes to.
d)
If Sally falls off the swing, she goes to the park.
96.
Which is the correct if-then statement for: "you will be late to school if you miss the bus."
a)
If you are late to school, then you will miss the bus.
b)
If you miss the bus, then you will be late to school
97.
This symbol, ∨, means?
a)
and
b)
or
c)
not
d)
implies
98.
This symbol, ∧, means?
a)
and
b)
or 
c)
not 
d)
implies
99.

If two lines do not intersect then they are coplanar and parallel, or skew. Lines AB and CD do not intersect.

a)

Lines AB and CD are parallel and not coplanar.

b)

Lines AB and CD are parallel and coplanar or they are skew.

c)

Lines AB and CD are skew.

d)

No Conclusion can be made.

100.

If there is lightening, then it is not safe to be out in the open. Mary sees lightening from her home.

a)

It is not safe for the lightening

b)

No conclusion can be made.

c)

It is not safe for Marty to be out in the open.

d)

There is lightening.

101.

If you go to the swimming pool, then you will enjoy yourself. If you enjoy yourself, you will want to return.

a)

If you return to the pool you will enjoy yourself.

b)

If you enjoy yourself, then you went to the pool.

c)

If you go to the pool, you will want to return.

d)

No conclusion can be made.

102.
Determine whether the stated conclusion is valid.
Given: If an animal is a dog, then they like biscuits.
Sammy is a dog.
Conclusion: Sammy likes biscuits.
a)
Invalid
b)
Valid
c)
Sammy is a Great Dane
d)
Sammy is really a cat.
103.
Draw a conclusion from the statement.
If you live in Orlando, then you live in Florida.
You live in Orlando.
a)
You live in Disney Land
b)
You are an old person.
c)
You live in Florida
d)
You live in Orlando
104.
Draw a conclusion from the statement.
If a whole number is even, then its square is divisible by 4.
The number I am thinking of is an even number.
a)
Then it's not odd.
b)
Then it's a whole number.
c)
Then its square is divisible by 4
d)
Then it's even.
105.
Use the Law of Detachment to draw a conclusion from the two given statements. If not possible, write not possible.
Statement 1: If I study for one hour each day, then I will score well on the exam
Statement 2: I will score well on the exam
a)
 I study for 1 hour each day.
b)
I do not study for 1 hour each day
c)
If I do well on the exam, I studied for 1 hour each day.
d)
not possible
106.
Use the law of syllogism to draw a conclusion from the two given statements:
Statement 1: If you exercise regularly, then you have a healthy body
Statement 2: If you have a healthy body, then you have more energy
a)
You have more energy
b)
If you exercise regularly, then you have more energy
c)
You have a healthy body
d)
If you do not have a healthy body, then you do not exercise regularly
107.

Which law of logic is this?

If I clean the bathroom, then I don't have to do the dishes.

I cleaned the bathroom.

Therefore, I don't have to do the dishes.

a)

Law of Detachment

b)

Law of Syllogism

c)

Law of Contrapositive

d)

None

108.
If an angle is 40⁰, then it is acute.
∠A is 40⁰.
Using the Law of Detachment, what is the logical statement to conclude?
a)
∠A is complementary to ∠B
b)
∠A is acute.
c)
∠A is obtuse.
d)
∠A is 40⁰
109.
Which is a valid conclusion from these statements?
If a quadrilateral is a rhombus, then it is a parallelogram.
If a quadrilateral is a parallelogram, then its opposite angles are congruent.
a)
Opposite angles of a quadrilateral are congruent
b)
Opposite angles of a rhombus are congruent
c)
Every quadrilateral is a rhombus
d)
Every parallelogram is a rhombus
110.
p→q
q→r
∴p→r
Which law is modeled?
a)
Law of Syllogism
b)
Law of Detachment
c)
Law of Contrapositive
d)
Law of Shannon
111.
p→q
p
∴q
Which law is modeled?
a)
Law of Syllogism
b)
Law of Detachment
c)
Law of Contrapositive
d)
Law of Shannon
112.

Write the statement below as a conditional statement.


Vertical Angles are congruent

a)

Two angles are vertical if and only if they are congruent.

b)

If two angles are congruent, then they are Vertical.

c)

If two angles are Vertical, then they are congruent.

113.

When writing a biconditional statement, we use the phrase ___ between the hypothesis and conclusion.

a)

if

b)

then

c)

if and only if

d)

always

114.
What is the biconditional that matches the statement: "A right angle is an angle with 90 degrees."
a)
If an angle has 90 degrees, then it is a right angle.
b)
If an angle is a right angle, then it has 90 degrees.
c)
An angle is a right angle if and only if it has 90 degrees.
115.
  Rewrite the following statement as a      biconditional: "Supplementary angles add up to 180"
a)
If two angles add up to 180o then they are supplementary.
b)
You can't it is conditional.
c)
Two angles are supplementary if and only if the sum of the measure of the two angles is 180o.
d)
If two angles sum does not equal 180o then they are not supplementary.
116.
Which is a counterexample for the following conditional:
If an electronic device has a screen then it is a television.
a)
television
b)
cell phone
c)
computer mouse
d)
keyboard
117.

Write the conditional statements as a biconditional statement:


1) If B is between A and C, then AB+BC=AC.

2) If AB+BC=AC, then B is between A and C.

a)

Segment Addition Postulate

b)

B is between A and C when AB+BC=AC if and only if Segment Addition Postulate.

c)

B is between A and C if and only if AB+BC=AC.

118.

What is the converse of the statement:

"If a number is divisible by 20, then it is even."

a)

A number divisible by 20 is even.

b)

If a number is even, then it is divisible by 20.

c)

If a number is not divisible by 20, then it is not even.

d)

If a number is not even, then it is not divisible by 20.

119.

What is the truth value of the converse of:

"If a number is divisible by 20, then it is even."

a)

True

b)

False

c)

Cannot be determined

120.
Which is a counterexample for the following conditional:
If an electronic device has a screen then it is a television.
a)
television
b)
cell phone
c)
computer mouse
d)
keyboard
121.

What is the converse of the statement:

"If x = 12, then 2x - 5 = 19"

a)

2x - 5 = 19

b)

If x≠12, then 2x − 5 ≠19If\ x\ne12,\ then\ 2x\ -\ 5\ \ne19

c)

If 2x − 5 = 19, then x = 12.If\ 2x\ -\ 5\ =\ 19,\ then\ x\ =\ 12.

d)

If 2x − 5 ≠ 19, then x ≠12.If\ 2x\ -\ 5\ \ne\ 19,\ then\ x\ \ne12.

122.

What is the truth value of the statement,  If 2x − 5 = 19, then x = 12.If\ 2x\ -\ 5\ =\ 19,\ then\ x\ =\ 12.  

a)

True

b)

False

c)

Cannot be determined

123.

Write the true biconditional for the statement:  If x = 12, then 2x − 5 = 19. If\ x\ =\ 12,\ then\ 2x\ -\ 5\ =\ 19.\  

a)

If 2x − 5 = 19, then x = 12. If\ 2x\ -\ 5\ =\ 19,\ then\ x\ =\ 12.\  

b)

x = 12 if and only if 2x − 5 = 19. x\ =\ 12\ if\ and\ only\ if\ 2x\ -\ 5\ =\ 19.\  

c)

x = 12 and 2x − 5 = 19. x\ =\ 12\ and\ 2x\ -\ 5\ =\ 19.\  

d)

This statement cannot be written as a true biconditional. 

124.

Test the statement below to see if it is reversible. If so, write it as a biconditional.

Complementary angles are two angles with measures that have a sum of 90.

a)

Reversible; If two angles are complementary, then the sum of their measures is 90.

b)

Reversible; Two angles are complementary if and only if the sum of their measures is 90.

c)

Not reversible.

125.

Which of the following statements are true biconditionals?

a)

x = 10 if and only if 3x + 2 = 28.

b)

3x + 2 = 11 if and only if x = 3.

c)

x2 = 25 if and only if x = −5.x^{2\ }=\ 25\ if\ and\ only\ if\ x\ =\ -5.

d)

x3=125 if and only if x = 5.x^3=125\ if\ and\ only\ if\ x\ =\ 5.

126.

Consider the statement:

If Julie eats tomatoes, then she likes salad.


Is the statement TRUE/FALSE/Cannot be determined?

a)

True

b)

False

c)

Cannot be determined

127.
When can a biconditional statement be true?
a)
When the inverse and the converse are both true
b)
When the original statement (conditional statement) & the contrapositive are both true.
c)
When the converse is true.
d)
When the original statement (conditional statement) and the converse are both true.
128.

Is the statement below a good definition? If not, explain.

A cat is an animal with whiskers.

a)

Good definition

b)

Not good: The statement is not reversible.

c)

Not good: The statement uses vague terms.

d)

Not good: The statement uses terms that are not clearly understood.

129.

Consider the statement:

If points are collinear, then they lie on the same line.


Is the statement TRUE/FALSE/Cannot be determined?

a)

True

b)

False

c)

Cannot be determined

130.

Is the statement below a good definition? If not, explain by checking all reasons that apply.

A segment is part of a line.

a)

Good definition

b)

Not good: The statement is not reversible.

c)

Not good: The statement uses vague terms.

d)

Not good: The statement uses terms that are not clearly understood.

131.

Is the statement below a good definition?

Perpendicular lines are two lines that intersect to form right angles.

a)

Good definition

b)

Not good: The statement is not reversible.

c)

Not good: The statement uses vague terms.

d)

Not good: The statement uses terms that are not clearly understood.

132.

Which conditional and its converse form a true biconditional statement?

a)

If x > 0, then ∣x∣>0.If\ x\ >\ 0,\ then\ \left|x\right|>0.

b)

If x = 3, then x2 = 9.If\ x\ =\ 3,\ then\ x^{2\ }=\ 9.

c)

If x3=5, then x = 125. If\ x^3=5,\ then\ x\ =\ 125.\

d)

If x = 19, then 2x − 3 = 35. If\ x\ =\ 19,\ then\ 2x\ -\ 3\ =\ 35.\

133.
What phrase does a biconditional statement use?
a)
if, then
b)
if, when
c)
if and only if
d)
then, if
134.
What is the biconditional that matches the statement: "A right angle is an angle with 90 degrees."
a)
If an angle has 90 degrees, then it is a right angle.
b)
If an angle is a right angle, then it has 90 degrees.
c)
An angle is a right angle if and only if it has 90 degrees.
135.

Is the following a good definition? Elephants are gigantic animals.

a)

Yes

b)

No, because elephants are not gigantic.

c)

No, because it is not written as a biconditional statement.

d)

No, because the converse of the conditional statement is false.

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