Free Printable Topic 1 Lessons 5 & 6 Review

Worksheets

Topic 1 Lessons 5 & 6 Review

Total questions: 93

Worksheet time: 8hrs 45mins

Name

Class

Date

Identify:

If p --> is true, and p occurs, then q occurs.

Law of Syllogism

Law of Contrapositives

Law of Detachment

Law of Diminishing Returns

Identify:

If p -->q is true, and q --> r is true, the p --> r is true.

Law of Syllogism

Law of Contrapositives

Law of Detachment

Law of Diminishing Returns

If possible use the Law of Detachment to make a conclusion.

If the band plays, then the people are happy.

The people are happy.

The band plays

The band didn't play

The people are not happy

Cannot determine

If possible use the Law of Syllogism to make a conclusion.

If Jon wins the contest, then he will get a lot of money.

If Jon gets a lot of money, then he will pay off his mortgage.

If Jon wins the contest, he will pay off his mortgage.

If Jon loses the contest, he will not pay off his mortgage.

If Jon pays off his mortgage, he will win the contest.

Cannot determine

If possible use the Law of Syllogism to make a conclusion.

If my teacher assigns homework, then I can't play video games.

If my teacher assigns homework, then I do it after school.

If my teacher assigns homework, then I play video games.

If I do my homework after school, then I can play video games.

If my teacher doesn't assign homework, then I can play video games.

Cannot determine

If possible use the Law of Detachment to make a conclusion.

If the doctor suspects a broken bone, then he will take an x-ray.

Lilly's arm is red and swollen, after falling off her bike.

The doctor will not take an x-ray.

The doctor will take an x-ray.

Lilly will not go to the doctor.

Cannot determine

If possible use the Law of Detachment and the Law of Syllogism to make a conclusion.

If a river is the longest in the region, then it is the longest on the continent.

If a river in the region is more than 1412 miles long, then it is the longest in the region.

The Calumet River is 1624 miles long.

The Amazon is the longest on the continent.

The Calumet River is not the longest in the region

The Calumet River is less than 1412 miles long.

The Calumet River is the longest on the continent.

If possible use the Law of Syllogism to make a conclusion.

If Dad works late, then we'll order take-out food.

If we order take-out food, then we'll get pizza.

If Dad works late, then we'll get pizza.

If Dad orders take-out, it will be pizza.

We will order Chinese.

Cannot determine

If possible use the Law of Detachment to make a conclusion.

If a student gets 5 tardies, then they will receive a detention.

Billy has a detention.

Billy has 6 tardies.

Billy is not in detention.

Billy has 5 tardies.

Cannot determine

10.

If possible use the Law of Detachment and the Law of Syllogism to make a conclusion.

If person lives in Chicago, then they live in Illinois.

If a person lives in Illinois, then they live in the Midwest.

Michael lives in Chicago.

Michael does not live in Illinois.

Michael lives in the Midwest.

Michael doesn't live in the Midwest.

Steve lives on the East Coast.

11.

What does deductive reasoning use to form its arguments?

patterns

specific cases

observed examples

facts, definitions, accepted properties, and laws of logic

12.

Use the Law of Detachment to determine what you can conclude from the given information, if possible.

If you passed the final, then you pass the class. You passed the final.

You passed the class.

You didn't pass the class

Not possible

13.

Use the Law of Detachment to determine what you can conclude from the given information, if possible.

If your parents let you borrow the car, then you will go to the movies with your friend. You will go to the movies with your friend.

Your parents let you borrow the car.

Your parents didn't let you borrow the car.

Not possible

14.

How would you describe the Law of Syllogism symbolically?

if p -> q is true and q is true, then p is true.

if p -> q is true and p is true, then q is true.

if p -> q is true and q -> r is true, then p -> r is true

15.

Use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements, if possible.

If a figure is a rhombus, then the figure is a parallelogram. If a figure is a parallelogram, then the figure is a quadrilateral.

If a figure is a rhombus, then the figure is a quadrilateral.

If a figure is a quadrilateral, then the figure is a rhombus.

Not possible

16.

Which law of logic is illustrated by these statements?

If you miss practice the day before a game, then you will not be a starting player in the game.

You miss practice on Tuesday. You will not start the game Wednesday.

Law of Detachment

Law of Syllogism

Speed Limit

None of the above

17.

Which law of logic is illustrated by the following statements?

If <1 and <2 are vertical angles, then <1 is congruent to <2. If <1 is congruent to <2, then m<1 = m<2.

If <1 and <2 are vertical angles, then m<1 = m<2.

Law of Detachment

Law of Syllogism

5th Amendment

Not possible

18.

If the school cafeteria sells pizza today, Greg is going to eat four pieces. Pizza is on sale for school lunch today.

Using deductive reasoning, what statement can you make based on this information?

Lots of people will buy pizza.

The school cafeteria sells pizza.

Greg will eat four pieces of pizza.

Greg needs to go on a diet.

19.

Using the statements:
If it is Friday, then I will get paid.
It is Friday.
Write the conclusion.

It is not Friday

It is Friday

I will not get paid

I will get paid

20.

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, then...

Look out for the snowplows while driving to school.

The big test will not be given today.

The roads will be hard to drive on.

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

21.

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.

Opposite angles of a quadrilateral are congruent

Opposite angles of a rhombus are congruent

Every quadrilateral is a rhombus

Every parallelogram is a rhombus

22.

Which statement is a valid conclusion based on the argument?
If a polygon is a regular pentagon, then the polygon has exactly five congruent angles.
The polygon is a regular pentagon.

Therefore, the polygon is a rectangle.

Therefore, the polygon is a regular quadrilateral.

Therefore, the polygon has exactly five congruent angles.

Therefore, the polygon has congruent sides.

23.

(1) If you drive safely, then the life you save may be your own.
(2) AJ drives safely.
(3) The life AJ saves may be his own.
Is statement (3) logical given the Law of Detachment, Syllogism, Contrapositive, or is it invalid?

Law of Detachment

Law of Syllogism

Law of Contrapositive

invalid

24.

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 is complementary to ∠B

∠A is acute.

∠A is obtuse.

∠A is 40⁰

25.

Use Law of Syllogism to make a conclusion.
If a number is divisible by 10, then it is divisible by 2. If a number is divisible by 2, then it is even.

If a number is divisible by 10, then it is even,

If a number is even, then it is divisible by 10.

If a number is divisible by 2, then it is even.

If a number is even, then it is divisible by 2.

26.

Use Law of Syllogism to make a conclusion.
If the perimeter of a square is 20 ft, then the length of a side is 5 ft.
If the length of a side of a square is 5 ft, then the area is 25 ft².

If the side of a square is 5 ft, then the perimeter is 20 ft.

If the perimeter of a square is 20 ft, then the area is 25 ft²

If the area of a square is 25 ft², then the side length is 5 ft.

If the are of a square is 25 ft², then the perimeter is 20 ft.

27.

Write the if-then statement that follows from the pair of true statements. If the sun is shining, then it is a beautiful day. If it is a beautiful day, then we will have a picnic.

If the sun is shining, then it is a beautiful day.

If it is a beautiful day, then the sun is shining.

If the sun is shining, then we will go on a picnic.

If we go on a picnic, then the sun is shining.

28.

Write the if-then statement that follows from the pair of true statements. If Todd goes to the movies, then Sarah will go to the movies. If Chris goes to the movies, then Todd will go to the movies.

If Chris goes to the movies, then Sarah will go to the movies.

If Todd goes to the movies, then Chris will go to the movies.

If Sarah goes to the movies, then Chris will go to the movies.

If Chris goes to the movies, then Todd will go to the movies.

29.

What can be concluded from the following statements?
If Tom goes fishing then he brings a pole.
If Tom brings his pole then he catches a fish.

If Tom goes fishing then he catches a fish.

If Tom brings his pole then he goes fishing

If Tom catches a fish then he brought his pole.

If Tom brings his pole then he catches a fish.

30.

Which of the following statements is valid based on the given scenario?
If Jason plays basketball, then Steve sits on the bench.
If Steve sits on the bench, then Ronald starts at center.

If Steve sits on the bench then Jason plays basketball.

If Ronald starts at center then Jason plays basketball.

If Steve sits the bench then Ronald does not start at center.

If Jason plays basketball then Ronald starts at center.

31.

By the Law of Detachment, what can you conclude from the statement?
If two planes intersect, then their intersection is a line.
Planes S and T intersect.

their intersection is a line

their intersection is a point

no conclusion can be made

the planes are parallel

32.

Determine if the conjecture is valid by the Law of Syllogism.
Given: If you are in California, then you are in the west coast. If you are Los Angeles, then you are in California.
Conjecture: If you are in Los Angeles, then you are in the west coast.

No, the conjecture is not valid.

Yes, the conjecture is valid.

33.

(1) If a figure is a square, then it is a polygon.
(2) Figure A is a polygon.
(3) ???????
What belongs in line 3?

Figure A is a polygon.

Figure A is a circle.

Figure A is a square.

invalid; nothing belongs in line 3

34.

IF an apple a day keeps the doctor away.

AND Joe ate an apple every day.

THEN

He will get a stomach ache

This makes no sense, what do apples have to do with doctors?

Joe will be spending lots of time at the dentists office

The doctor will stay away

35.

Using the Law of Detachment, what can you conclude?
If you earn more than $14, then you can buy a new CD.
You earn $15.

you can buy a new CD

you cannot buy a new CD

no conclusion can be made

you earn more than $14

36.

Draw a conclusion from the statement.
Given: If you are at least 25 year old, then you can rent a car.
Clay can rent a car.
Conclusion: ?

Clay is at least 25 years old

Clay can rent a car

Clay can go on a road trip

Invalid

37.

Inductive Reasoning means...

Guessing

Testing and observing patterns to make conjectures

Explaining why

38.

Since all humans are mortal, and I am human, then I am mortal.

Deductive

Inductive

39.

All chickens that we have seen have been brown; so, all chickens are brown.

Deductive

Inductive

40.

Which law of logic is illustrated by these statements?

If you miss practice the day before a game, then you will not be a starting player in the game.

You miss practice on Tuesday. You will not start the game Wednesday.

Law of Detachment

Law of Syllogism

Speed Limit

None of the above

41.

Draw a conclusion from the statement.

If Jack goes to school, then it is Monday.

Jack doesn't go to school.

Jack skipped school.

It isn't Monday.

It's Saturday.

Invalid: We can't make any conclusion.

42.

p→q
q→r
∴p→r
Which law is modeled?

Law of Syllogism

Law of Detachment

Law of Contrapositive

Law of Shannon

43.

p→q
p
∴q
Which law is modeled?

Law of Syllogism

Law of Detachment

Law of Contrapositive

Law of Shannon

44.

Identify the hypothesis and conclusion of the conditional statement:
If you give me twenty dollars, then I will be your best friend.

Hypothesis: I will be your best friend
Conclusion: you give me twenty dollars

Hypothesis: you give me twenty dollars
Conclusion: I will be your best friend

Hypothesis: if you have to pay for friends
Conclusion: then you probably should reevaluate your life

Hypothesis: you will not have to pay twenty dollars
Conclusion: if you have lots of friends

45.

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

If I have a Siberian Husky.

I have a Siberian Husky.

Then I have a dog.

HI have a dog.

46.

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

If the angles are congruent.

The angles are congruent.

Then the measures of the angles are equal.

The measures of the angles are equal.

47.

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

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

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

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

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

48.

Is this statement true?

True. Class can't happen if a chair isn't occupied.

False. There are empty chairs here.

True.

True. There are no chairs here, so the hypothesis is true.

49.

When forming the converse we ___________ the hypothesis and conculsion

negate

switch

highlight

switch and negate

50.

When forming the contrapositive we ___________ the hypothesis and conculsion

negate

switch

highlight

switch and negate

51.

When forming the inverse we ___________ the hypothesis and conculsion

negate

switch

highlight

switch and negate

52.

Which is the correct if-then statement for: "you will be late to school if you miss the bus."

If you are late to school, then you will miss the bus.

If you miss the bus, then you will be late to school

If you sleep late, then you don't have to go to school.

If you miss the bus, then you'll have to walk and be late.

53.

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

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

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

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

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

54.

Original: If Emily is not late to class, then she will not be marked tardy.
What is this? If Emily is late to class, then she will be marked tardy.

Converse

Inverse

Contrapositive

Negation

55.

Which of the following is the inverse to the statement:
"If you diet and exercise, then you will lose weight."

If you don't diet and exercise, then you will not lose weight.

If you don't diet and exercise, then you will lose weight.

If you lose weight, then you dieted and exercised.

If you don't lose weight, then you diet and exercise.

56.

What is this?

Conditional Statement

Inverse

Converse

THIS IS A GEOMETRY CLASS!!! GIVE ME NUMBERS!

57.

p→q
What is the converse?

q→p

∼p→∼q

∼q→∼p

p→∼q

58.

What is the hypothesis of the given Conditional Statement?

Jimmy will go to Orlando

Jimmy goes on vacation

Jimmy will go to Orlando

Who is Jimmy?

59.

What is the conclusion to this?

Clarkson will be the coolest

Clarkson will not be the coolest

Clarkson gives us Mountain Dew

Clarkson will not give us Mountain Dew

60.

What is the converse to this statement?

If it isn't dark outside, then it is not night.

If it is night, then it is dark outside

If it is not night, then it is not dark outside.

It is night.

61.

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

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

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

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

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

62.

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

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

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

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

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

63.

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

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

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

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

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

64.

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

If I have a Siberian Husky.

I have a Siberian Husky.

Then I have a dog.

I have a dog.

65.

Which statement has a true truth value?

Fish can walk

Chicken has four legs.

Birds can fly.

Shark has two legs.

66.

Conditional: If Maria gets married, then the reception will be at the country club.
What is this statement: If the reception is at the country club, then Maria will be getting married.

Converse

Inverse

Contrapositive

Negation

67.

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

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

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

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

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

68.

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

If the angles are congruent.

The angles are congruent.

Then the measures of the angles are equal.

The measures of the angles are equal.

69.

What is the conclusion of the following statement: "The angles are supplementary, if they add up to 180 degrees."

if they add up to 180 degrees

the angles are supplementary

they add up to 180 degrees

there is no conclusion

70.

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

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

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

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

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

71.

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

If angles are congruent.

Angles are congruent.

Then the measures of the angles are equal.

The measures of the angles are equal.

72.

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

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

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

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

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

73.

Is the inverse of this true?

It's true. If two angles are not supplementary, then they do not add up to 180 degrees.

It's false. If angles don't add up to 180, they can still be supplementary.'

It's false. Supplementary angles add up to 90 degrees.

It's true. Supplementary angles can add up to less than 180 degrees.

74.

Write the following statement in if-then form.
All students at Hermitage take an English class.

If you take an English class, then you are a student at Hermitage.

If you are a student at Hermitage, then you take an English. class

75.

What is the converse of the following statement?
If it is Saturday, then the school is closed

If the school is closed, then it is Saturday.

If it is not Saturday, then the school is not closed.

If the school is not closed, then it is not Saturday.

76.

What is the contrapositive of the following statement?
If it is Saturday, then the school is closed

If the school is closed, then it is Saturday.

If it is not Saturday, then the school is not closed.

If the school is not closed, then it is not Saturday.

77.

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.

Converse

Inverse

Contrapositive

Negation

78.

What does this mean?

Conditional Statement

Inverse Statement

Converse Statement

Contrapositive Statement

79.

What does this mean?

Conditional Statement

Converse

Inverse

Contrapositive

80.

What is the conclusion to the statement?

You like fried chicken

You only like fried chicken from KFC

You like KFC

You hate KFC

81.

What is the hypothesis of this conditional?

Sally goes to the park.

Sally will fall off the swing.

Parks don't have swings that Sally goes to.

If Sally falls off the swing, she goes to the park.

82.

What is it hypothesis in the statement:" If today is Tuesday, then we have school."?

Tomorrow is Wednesday.

We have school.

Today is Tuesday.

We do not have school.

83.

Write the conclusion of the statement,

"If you are Anthony Rizzo, then you are a Chicago Cub."

You are Anthony Rizzo.

You are a Chicago Cub.

The Cubs are the best.

84.

What are the two parts of a conditional statement?

Hypothesis

Conclusion

Converse

Inverse

85.

What is the negation of "x > 3"?

$x=3$

$x\le3$

$x<3$

86.

Write the converse of
$If\ 3x\ =\ 15,\ then\ x\ =\ 5.\$

$If\ x\ \ne5,\ then\ 3x\ \ne15.$

$If\ x\ =\ 5,\ then\ 2x\ =\ 10.$

$If\ \ 3x\ \ne15,\ then\ x\ne5.$

$If\ x\ =\ 5,\ then\ 3x\ =\ 15.\$

87.

Write the inverse of
$If\ 3x\ =\ 15,\ then\ x\ =\ 5.\$

$If\ x\ \ne5,\ then\ 3x\ \ne15.$

$If\ x\ =\ 5,\ then\ 2x\ =\ 10.$

$If\ \ 3x\ \ne15,\ then\ x\ne5.$

$If\ x\ =\ 5,\ then\ 3x\ =\ 15.\$

88.

Write the contrapositive of
$If\ 3x\ =\ 15,\ then\ x\ =\ 5.\$

$If\ x\ \ne5,\ then\ 3x\ \ne15.$

$If\ x\ =\ 5,\ then\ 2x\ =\ 10.$

$If\ \ 3x\ \ne15,\ then\ x\ne5.$

$If\ x\ =\ 5,\ then\ 3x\ =\ 15.\$

89.

Rewrite the statement as a conditional statement.

"The sum of the angles of a triangle is 180."

If the sum of the angles of a triangle, then 180.

If a figure is a triangle, then the sum of the angles is 180.

If a figure sums angles, then the triangle is 180.

90.

Write the converse of the following statement.

"If a figure is a triangle, then the angles add to 180.

If a figure is not a triangle, then the angles do not add to 180.

If the angles of a figure do not add to 180, then it is not a triangle.

If a figure has angles that add to 180, then it is a triangle.

91.

Write the contrapositive of the following statement.

"If a figure is a triangle, then the angles add to 180.

If a figure is not a triangle, then the angles do not add to 180.

If the angles of a figure do not add to 180, then it is not a triangle.

If a figure has angles that add to 180, then it is a triangle.

92.

Write the inverse of the following statement.

"If a figure is a triangle, then the angles add to 180.

If a figure is not a triangle, then the angles do not add to 180.

If the angles of a figure do not add to 180, then it is not a triangle.

If a figure has angles that add to 180, then it is a triangle.

93.

Rewrite the statement as a conditional statement.

"All dolphins are mammals."

If a dolphin, then a mammal.

If an animal is a dolphin, then it is a mammal.

If an animal is a mammal, then it is a dolphin.

If an animal is not a mammal, then it is not a dolphin.

Reset

Topic 1 Lessons 5 & 6 Review

Total questions: 93

Worksheet time: 8hrs 45mins

Similar Resources on Wayground