Quiz about Conditional Statements, Inductive, and Deductive Reasoning

Question 1

Which of the following is a conditional statement?

Accepted Answer

If an integer is an even number, then it is divisible by 2.

Answer

All even numbers are divisible by 2.

Answer

If an even number is divisible by 2.

Answer

Then even numbers are divisible by 2.

Question 2

How do you write the converse of a conditional statement?

Accepted Answer

Reverse the hypothesis and conclusion

Answer

Negate the hypothesis and conclusion

Answer

Negate and reverse the hypothesis and conclusion

Answer

Take it to Journeys and buy the converses.

Question 3

Which is the inverse of the given statement:

"If you are human, then you are mortal."

Accepted Answer

If you are not human, then you are not mortal.

Answer

If you are mortal, then you are human.

Answer

You are human if and only if you are mortal.

Answer

If you are not mortal, then you are not human.

Question 4

What do you call the first part of a conditional statement that follows the word "if"?

Accepted Answer

hypothesis

Answer

conclusion

Answer

hypnosis

Answer

conjunction

Question 5

What do you call the second part of a conditional statement that follows the word "then"?

Accepted Answer

conclusion

Answer

hypothesis

Answer

conjecture

Answer

hypoallergenic

Question 6

Which of the following is the contrapositive of the given statement:

"If you are human, then you are mortal."

Accepted Answer

If you are not mortal, then you are not human.

Answer

If you are not human, then you are not mortal.

Answer

If you are mortal, then you are human.

Answer

You are human if and only if you are mortal.

Question 7

Negate the following statement:

"I love geometry."

Accepted Answer

I do not love geometry

Answer

Geometry I love

Answer

If and only if I love geometry

Answer

If I love geometry, then I do not love geometry.

Question 8

Which of the following DOES NOT describe inductive reasoning?

Accepted Answer

process of reasoning based on known facts

Answer

reaches conclusion based on a pattern of specific examples

Answer

reaches conclusion based on past events

Answer

starts with an observation and works its way up

Question 9

Which of the following DOES NOT describe deductive reasoning?

Accepted Answer

starts with an observation and works its way up

Answer

process of reasoning based on known facts

Answer

starts with a hypothesis and works its way down

Answer

uses evidence to reach a logical conclusion

Question 10

Find the next term:

3, 5, 9, 15, 23, . . .

Accepted Answer

33

Answer

35

Answer

25

Answer

31

Question 11

Which algebraic expression generalizes the pattern for the nth term?

Accepted Answer

n2

Answer

2n

Answer

n+3

Answer

2n-1

Question 12

Give a counter example to the following statement:

"All odd numbers are prime numbers."

Accepted Answer

15

Answer

3

Answer

11

Answer

7

Question 13

Give a counter example to the following statement:

"If candy is crunchy, then it contains nuts."

Accepted Answer

Nerds

Answer

Snickers Bar

Answer

Pixy Stix

Answer

Almond Joy

Question 14

Which of the following phrases can be found in a biconditional statement?

Accepted Answer

if and only if

Answer

supercalifragilisticexpialidocious

Answer

if then

Answer

if it implies

Question 15

Which law states that if a conditional statement is true and its hypothesis is true, then its conclusion must also be true?

Accepted Answer

Law of Detachment

Answer

Law of Detainment

Answer

Law of Syllogism

Answer

Law of Syllables

Question 16

Which law states that given 2 true conditionals with the conclusion of the first being the hypothesis of the second, there exists a third true conditional having the hypothesis of the first and the conclusion of the second?

Accepted Answer

Law of Syllogism

Answer

Law of Detachment

Answer

Law of Determination

Answer

Law of Solilquy

Question 17

If the argument is valid, determine by which law statement 3 follows from statements 1 and 2.

(1) If you are over 54 inches tall, then you can ride the roller coaster.

(2) Cindy is 56 inches tall.

(3) Cindy can ride the roller coaster.

Accepted Answer

Law of Detachment

Answer

Law of Contrapositive

Answer

Law of Syllogism

Answer

Invalid Argument

Question 18

If the argument is valid, determine by which law statement 3 follows from statements 1 and 2.

(1) If you ride your bike to school, then you exercise.

(2) If you exercise, then you are happy.

(3) If you ride your bike to school, then you are happy.

Accepted Answer

Law of Syllogism

Answer

Law of Biconditionals

Answer

Law of Detachment

Answer

Invalid Argument

Question 19

If the argument is valid, determine by which law statement 3 follows from statements 1 and 2.

(1) If you loose a tooth, then the tooth fairy will bring you money.

(2) John has money.

(3) John lost a tooth.

Accepted Answer

Invalid Argument

Answer

Law of Symbolism

Answer

Law of Syllogism

Answer

Law of Detachment

Question 20

Write the following as a conditional statement:

"Rain makes the grass grow."

Accepted Answer

If it is raining, then the grass will grow.

Answer

The grass will grow only if it rains.

Answer

If rain makes the grass grow.

Answer

If it does not rain, then the grass will not grow.

Question 21

Write the following statement as a conditional statement:

A dog with proper training will not misbehave.

Accepted Answer

If a dog has proper training, then it will not misbehave.

Answer

If a dog does not behave, then it had proper training.

Answer

A dog had proper training if and only if it will not misbehave.

Question 22

What is a conjecture?

Accepted Answer

A statement believed to be true based on observations.

Answer

An example which disproves an hypothesis.

Answer

A statement that reverses the hypotheses and the conclusion.

Question 23

This is used to prove that a conjecture is false.

Accepted Answer

Counterexample

Answer

Inductive Reasoning

Answer

Concluding statement

Answer

Negation

Question 24

Which number is a counterexample to the following statement? :
All numbers that are divisible by 2 are divisible by 4

Accepted Answer

42

Answer

0

Answer

12

Answer

28

Question 25

Deductive reasoning means...

Accepted Answer

Drawing conclusions from situations based on facts and definitions

Answer

Guessing without any information

Answer

Sounding knowledgeable even when you are not

Answer

Testing and observing patterns to make conjectures

Question 26

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 27

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 28

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.

Accepted Answer

Inverse

Answer

Converse

Answer

Contrapositive

Answer

Negation

Question 29

What is this mean? (Given the original p --> q)

Accepted Answer

Contrapositive

Answer

Conditional Statement

Answer

Converse

Answer

Inverse

Question 30

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.

Accepted Answer

Converse

Answer

Inverse

Answer

Contrapositive

Answer

Negation

Question 31

Which two statements make up the following biconditionals: "A polygon is a triangle if and only if it has exactly 3 sides."

Accepted Answer

1. If a polygon is a triangle, then the polygon has exactly three sides. 2. If a polygon has exactly three sides then it is a triangle

Answer

1. If a polygon is not a triangle, then the polygon does not have three side. 2. If a polygon does not have three sides, then it is not a triangle.

Answer

1. A polygon is a triangle. 2. The polygon has three sides.

Question 32

How can you combine the following statements as a biconditional? If this month is June, then next month is July. If next month is July, then this month is June.

Accepted Answer

This month is June if and only if the next month is July.

Answer

This month is not June if and only if the next month is not July.

Answer

If this month is July, then the previous month was June.

Answer

This month is July if and only if the previous month was June.

Question 33

When can a biconditional statement be written?

Accepted Answer

When the original statement (conditional statement) and the converse are both true.

Answer

When the inverse and the converse are both true

Answer

When the original statement (conditional statement) & the contrapositive are both true.

Answer

When the converse is true.

Question 34

"A bird is an animal that flies" is not a good definition because:

Accepted Answer

It and its converse are not true.

Answer

It does not use clearly understood terms.

Answer

It and its contrapositive are not true.

Answer

It and its inverse are not true.

Question 35

Make a conclusion.

1. If a number is divisible by 10, then it is divisible by 2.

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 36

The Giants have lost their last seven games. Thus, they will probably lose their next game.

What type of reasoning was used?

Accepted Answer

Inductive

Answer

Deductive

Question 37

All students go to school. You are a student. Therefore you go to school.

What type of reasoning was used?

Accepted Answer

Deductive

Answer

Inductive

Question 38

Since it rained every christmas day for the past four years it will rain on christmas day this year.

What type of reasoning was used?

Accepted Answer

Inductive

Answer

Deductive

Question 39

A child examines ten tulips from a crop, all of them are red, and concludes that all tulips must be red.

What type of reasoning was used?

Accepted Answer

Inductive

Answer

Deductive

Question 40

Oviparous animals are animals that lay their eggs, Clarke has a platypus. Clarke went to clean up her platypus' nest this morning and saw a pair of eggs, so she concluded that a platypus is an oviparous animal.

What type of reasoning was used?

Accepted Answer

Deductive

Answer

Inductive

Question 41

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 42

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 43

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 44

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.

Accepted Answer

Then its square is divisible by 4

Answer

Then it's not odd.

Answer

Then it's a whole number.

Answer

Then it's even.

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 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.

Accepted Answer

Law of Detachment

Answer

Law of Syllogism

Answer

Law of Contrapositive

Answer

None

Question 47

Write the statement below as a conditional statement.

Vertical Angles are congruent

Accepted Answer

If two angles are Vertical, then they are congruent.

Answer

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

Answer

If two angles are congruent, then they are Vertical.

Question 48

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.

Accepted Answer

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

Answer

Segment Addition Postulate

Answer

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

Question 49

What is the conclusion that you can infer from these two premises below:

All tigers are cat

All cats are animals

Therefore the conclusion is .................................

Accepted Answer

All tigers are animals

Answer

Cat are tigers

Answer

Animals are cats

Answer

Cat are tigers

Question 50

All birds have wings

No humans have wings

Thus the conclusion is ..........................................

Accepted Answer

No humans are birds.

Answer

Birds and humans have wings

Answer

birds are humans

Answer

Birds and humans are different

Question 51

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

If the band plays, then the people are happy.

The people are happy.

Accepted Answer

Cannot determine

Answer

The band plays

Answer

The band didn't play

Answer

The people are not happy

Question 52

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.

Accepted Answer

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

Answer

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

Answer

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

Answer

Cannot determine

Question 53

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.

Accepted Answer

Cannot determine

Answer

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

Answer

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

Answer

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

Question 54

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.

Accepted Answer

The doctor will take an x-ray.

Answer

The doctor will not take an x-ray.

Answer

Lilly will not go to the doctor.

Answer

Cannot determine

Question 55

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.

Accepted Answer

The Calumet River is the longest on the continent.

Answer

The Amazon is the longest on the continent.

Answer

The Calumet River is not the longest in the region

Answer

The Calumet River is less than 1412 miles long.

Question 56

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.

Accepted Answer

Michael lives in the Midwest.

Answer

Michael does not live in Illinois.

Answer

Michael doesn't live in the Midwest.

Answer

Steve lives on the East Coast.

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