Quiz about Chapter 2 Review (8DA)

Question 1

Inductive reasoning goes from _ to _

Accepted Answer

Specific to general

Answer

General to specific

Question 2

Deductive reasoning goes from _ to _

Accepted Answer

General to specific

Answer

Specific to general

Question 3

What type of reasoning explains the next terms? 3, 9, 27, _

Accepted Answer

Inductive

Answer

Deductive

Question 4

What's the next terms in the sequence? 3, 9, 27, _

Accepted Answer

81

Answer

36

Answer

243

Answer

49

Question 5

What is a conjecture?

Accepted Answer

A conclusion reached from inductive reasoning

Answer

An educated guess

Answer

A prediction

Answer

A counterexample to a counterexample

Question 6

Circle with 1 diameter has 2 parts, 2 diameters have 4 parts, 3 diameters have 6 parts. Make a conjecture about a circle with 5 diameters.

Accepted Answer

It will have 10 parts

Answer

It will have 25 parts

Answer

It will have 5 parts

Answer

It will have 50 parts

Question 7

How many counterexamples do you need to prove a conjecture false?

Accepted Answer

1

Answer

0

Answer

3 (the minimum for scientific proof)

Answer

An equal amount to the number of conjectures

Question 8

Mark runs a mile in 6 mins. If your mile time is less than 8 mins, then you can be on the team. Mark is on the team. What type of reasoning is this?

Accepted Answer

Deductive reasoning

Answer

Inductive reasoning

Question 9

All speeders are ticketed. Jim is a speeder. Jim was ticketed.

Accepted Answer

Deductive reasoning

Answer

Inductive reasoning

Question 10

1, 2, 6, 24, 120, _

Accepted Answer

720

Answer

500

Answer

480

Answer

1030

Question 11

Conditional: If _, then _

Accepted Answer

Hypothesis, Conclusion

Answer

Conclusion, Hypothesis

Answer

Converse, Inverse

Answer

Contrapositive, Conditional

Question 12

If p->q, what's the converse?

Accepted Answer

q --> p

Answer

~p --> ~q

Answer

~q --> ~p

Answer

p->q

Question 13

If p->q, what's the inverse?

Accepted Answer

~p --> ~q

Answer

q --> p

Answer

~q --> ~p

Answer

p->q

Question 14

If p->q, what's the contrapositive?

Accepted Answer

~q --> ~p

Answer

~p --> ~q

Answer

q --> p

Answer

p --> q

Question 15

If the conditional is true, then the _ is also always true

Accepted Answer

Contrapositive

Answer

Converse

Answer

Inverse

Answer

Conditional

Question 16

If the converse is false, then the _ is also always false

Accepted Answer

Inverse

Answer

Converse

Answer

Contrapositive

Answer

Conditional

Question 17

If the contrapositive is false, then the _ is also always false

Accepted Answer

Conditional

Answer

Converse

Answer

Inverse

Answer

Contrapositive

Question 18

If the inverse is true, then the _ is also always true

Accepted Answer

Converse

Answer

Inverse

Answer

Contrapositive

Answer

Conditional

Question 19

Write a conditional for the given diagram

Accepted Answer

If an integer is divisible by 8, then it is divisible by 2

Answer

If an integer is divisible by 2, then it is divisible by 8

Question 20

Write a conditional for the given diagram

Accepted Answer

p --> q

Answer

q --> p

Question 21

T of F?

Accepted Answer

T

Answer

F

Question 22

T or F?

Accepted Answer

F, T, F

Answer

F, F, F

Answer

T, T, T

Answer

T, F, T

Question 23

T or F?

Accepted Answer

F, T, F

Answer

F, F, F

Answer

T, T, T

Answer

T, F, T

Question 24

T or F?

Accepted Answer

T, T, F

Answer

F, T, F

Answer

F, T, T

Answer

T, F, T

Question 25

T or F?

Accepted Answer

T, T, T

Answer

F, T, T

Answer

T, F, T

Answer

T, T, F

Question 26

T or F?

Accepted Answer

F, F

Answer

T, T

Answer

F, T

Answer

T, F

Question 27

T or F?

Accepted Answer

T, F

Answer

T, T

Answer

F, T

Answer

F, F

Question 28

B <--> Q is true, if

Accepted Answer

B -> Q AND Q -> B are both true

Answer

B -> Q OR Q -> B are both true

Answer

All B and all Q values are true

Answer

~B and ~Q are false

Question 29

A mathematical definition is a/an _

Accepted Answer

Biconditional

Answer

Conditional

Answer

Conclusion

Answer

Conjecture

Question 30

The last line in a proof is always the...

Accepted Answer

Prove

Answer

Given

Answer

Conditionals

Answer

Equations

Question 31

The first line in a proof is always the...

Accepted Answer

Given

Answer

Prove

Answer

Conditionals

Answer

Equations

Question 32

Angles _ & _ are congruent

Accepted Answer

2 & 4

Answer

1 & 2

Answer

2 & 3

Answer

4 & 1

Question 33

Angles _ & _ are congruent

Accepted Answer

1 & 3

Answer

1 & 2

Answer

2 & 3

Answer

4 & 1

Question 34

How can you prove step #2?

Accepted Answer

Vertical angle theorem

Answer

Subtraction property of equality

Answer

Transitive property of congruence

Answer

Definition of supplementary angles

Question 35

How can you prove step #4?

Accepted Answer

Vertical angle theorem

Answer

Subtraction property of equality

Answer

Transitive property of congruence

Answer

Definition of supplementary angles

Question 36

How can you prove step #5?

Accepted Answer

Transitive property of congruence

Answer

Vertical angle theorem

Answer

Subtraction property of equality

Answer

Definition of supplementary angles

Question 37

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

Accepted Answer

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

Answer

Lines AB and CD are parallel and not coplanar.

Answer

Lines AB and CD are skew.

Answer

No Conclusion can be made.

Question 38

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

Accepted Answer

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

Answer

It is not safe for the lightening

Answer

No conclusion can be made.

Answer

There is lightening.

Question 39

If we see John on Monday, then we can ask him over for lunch. We see John on Monday.

Accepted Answer

We asked John to have lunch with us.

Answer

John may eat with us.

Answer

John saw us on Monday

Answer

No conclusion can be made since the hypothesis did not occur.

Question 40

If two planes intersect, then their intersection is a line. If two planes are not parallel, then they intersect.

Accepted Answer

If two planes are not parallel, then their intersection is a iine.

Answer

No Conclusion can be made.

Answer

If two planes intersect they are not parallel.

Answer

If two planes are parallel, then they do not intersect.

Question 41

If it rains on Tuesday we will not go to the park on Tuesday.

If we do not go to the park on Tuesday we will go on Wednesday.

Accepted Answer

If it rains on Tuesday, we will go Wednesday.

Answer

If we go to the park on Wednesday, then it rained on Tuesday.

Answer

No conclusion can be made.

Answer

If we go to the park on Tuesday, then it rained on Tuesday.

Question 42

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

Accepted Answer

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

Answer

If you return to the pool you will enjoy yourself.

Answer

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

Answer

No conclusion can be made.

Question 43

If the sun is shining it is a beautiful day. If it is a beautiful day then we will go go hiking.

Accepted Answer

If the sun is shining then we will go hiking.

Answer

If the sun is not shining, we will not go hiking.

Answer

No conclusion can be made.

Answer

If we go hiking, then it is a beautiful day.

Question 44

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

Accepted Answer

If you exercise regularly, then you have more energy

Answer

You have more energy

Answer

You have a healthy body

Answer

If you do not have a healthy body, then you do not exercise regularly

Question 45

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

Accepted Answer

not possible

Answer

I study for 1 hour each day.

Answer

I do not study for 1 hour each day

Answer

If I do well on the exam, I studied for 1 hour each day.

Question 46

Which law of deductive reasoning is being used, if any?
If a triangle is equilateral, then all three sides are congruent.
If all the sides of a triangle are congruent, then the angles opposite them are congruent.
Therefore, if a triangle is equilateral, then the angles opposite the sides are congruent.

Accepted Answer

Law of Syllogism

Answer

Law of Detachment

Answer

Law of the Contrapositive

Answer

Not valid

Question 47

Using the Law of Syllogism, which of the following completes the statement to form a valid conclusion?
If it is snowing heavily, then school will be canceled.
If school is canceled, the big test will not be given today.
It is snowing heavily, therefore

Accepted Answer

the big test will not be given today.

Answer

look out for the snowplows while driving to school.

Answer

the roads will be hard to drive on.

Answer

you should call the school to see if school is canceled.

Question 48

Which law of deductive reasoning is being used, if any?
If a triangle is equilateral, then all three sides are congruent.
If all the sides of a triangle are congruent, then the angles opposite them are congruent.
Therefore, if a triangle is equilateral, then the angles opposite the sides are congruent.

Accepted Answer

Law of Syllogism

Answer

Law of Detachment

Answer

Law of the Contrapositive

Answer

Not valid

Question 49

Which law of logic is this:
If I buy a dress, then I won't get chips.
I bought a dress.
Therefore, I won't get chips.

Accepted Answer

Law of Detachment

Answer

Law of Contrapositive

Answer

Law of Syllogism

Answer

Law of Biconditional

Question 50

If Mrs. Hafner walks dogs at the animal shelter, then she has a late dinner. If it is Wednesday, then Mrs. Hafner walks dogs at the animal shelter.

What can you conclude?

Accepted Answer

If it is Wednesday, then Mrs. Hafner has a late dinner.

Answer

Nothing

Answer

If Mrs. Hafner has a late dinner, then she walks dogs at the animal shelter.

Answer

If Mrs. Hafner has a late dinner, then it is Wednesday.

Question 51

If it is Monday, then Garfield is grumpy. If it is Monday, then John will feel Garfield lasagna.

What can you conclude?

Accepted Answer

Nothing

Answer

If Garfield is grumpy, then John will feed Garfield lasagna.

Answer

Garfield is grumpy, if it is Monday.

Answer

If John feeds Garfield lasagna, then it is Monday.

Question 52

If a figure is a square, then it is a rectangle. If a figure is a rectangle, then it has 4 right angles.

What can you conclude?

Accepted Answer

If a figure is a square, then it has 4 right angles.

Answer

If a figure has 4 right angles, then it is a square.

Answer

Nothing

Answer

If a figure is a rectangle, then it is a square with 4 right angles.

Question 53

If Bill wears a green shirt, then he will pass the test. Bill wore a green shirt.

What can you conclude?

Accepted Answer

Bill passed the test.

Answer

Bill wore a green shirt.

Answer

Nothing

Question 54

If it is rainy outside, then the sun is behind clouds. The sun is behind the clouds.

What can you conclude?

Accepted Answer

Nothing

Answer

It is rainy outside.

Answer

If it is rainy outside, then the sun is behind the clouds.

Question 55

If Carly runs a 5k, then she will be tired. Carly is tired.

What can you conclude?

Accepted Answer

Nothing

Answer

Carly runs a 5k.

Question 56

Given, "If I have a Siberian Husky, then I have a dog." Identify the converse.

Accepted Answer

If I have a dog, then I have a Siberian Husky.

Answer

If I do not have a Siberian Husky, then I do not have a dog.

Answer

If I do not have a dog, then I do not have a Siberian Husky.

Answer

If I do not have a Siberian Husky, then I have a dog.

Question 57

Given, "If I have a Siberian Husky, then I have a dog." Identify the inverse.

Accepted Answer

If I do not have a Siberian Husky, then I do not have a dog.

Answer

If I have a dog, then I have a Siberian Husky.

Answer

If I do not have a dog, then I do not have a Siberian Husky.

Answer

If I do not have a Siberian Husky, then I have a dog.

Question 58

Given, "If I have a Siberian Husky, then I have a dog." Identify the contrapositive.

Accepted Answer

If I do not have a dog, then I do not have a Siberian Husky.

Answer

If I do not have a Siberian Husky, then I do not have a dog.

Answer

If I have a dog, then I have a Siberian Husky.

Answer

If I do not have a Siberian Husky, then I have a dog.

Question 59

Given, "If I have a Siberian Husky, then I have a dog." Identify the conclusion.

Accepted Answer

I have a dog.

Answer

If I have a Siberian Husky.

Answer

I have a Siberian Husky.

Answer

Then I have a dog.

Question 60

Given, "If angles are congruent, then the measures of the angles are equal." Identify the converse.

Accepted Answer

If the measures of the angles are equal, then the angles are congruent.

Answer

"If angles are not congruent, then the measures of the angles are not equal."

Answer

If the measures of the angles are not equal, then the angles are not congruent.

Answer

If the angles are not congruent, then the measure of the angles are equal.

Question 61

Given, "If angles are congruent, then the measures of the angles are equal." Identify the inverse.

Accepted Answer

"If angles are not congruent, then the measures of the angles are not equal."

Answer

If the measures of the angles are equal, then the angles are congruent.

Answer

If the measures of the angles are not equal, then the angles are not congruent.

Answer

If the angles are not congruent, then the measure of the angles are equal.

Question 62

Given, "If angles are congruent, then the measures of the angles are equal." Identify the contrapositive.

Accepted Answer

If the measures of the angles are not equal, then the angles are not congruent.

Answer

If the measures of the angles are equal, then the angles are congruent.

Answer

If angles are not congruent, then the measures of the angles are not equal.

Answer

If the angles are not congruent, then the measure of the angles are equal.

Question 63

Given, "If angles are congruent, then the measures of the angles are equal." Identify the hypothesis.

Accepted Answer

Angles are congruent.

Answer

If angles are congruent.

Answer

Then the measures of the angles are equal.

Answer

The measures of the angles are equal.

Question 64

Given, "If angles are congruent, then the measures of the angles are equal." Identify the conclusion.

Accepted Answer

The measures of the angles are equal.

Answer

If the angles are congruent.

Answer

The angles are congruent.

Answer

Then the measures of the angles are equal.

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