Quiz about Unit 2: Logic Review

Question 1

$$p\rightarrow q$$ is the symbolic notation for:

Accepted Answer

Conditional Statements

Answer

Converse Statements

Answer

Inverse Statements

Answer

Contrapositive Statements

Answer

Biconditional Statements

Question 2

$$q\rightarrow p$$ is the symbolic notation for:

Accepted Answer

Converse Statements

Answer

Conditional Statements

Answer

Inverse Statements

Answer

Contrapositive Statements

Answer

Biconditional Statements

Question 3

$$\sim q\rightarrow\sim p$$ is the symbolic notation for:

Accepted Answer

Contrapositive Statements

Answer

Conditional Statements

Answer

Converse Statements

Answer

Inverse Statements

Answer

Biconditional Statements

Question 4

$$\sim p\rightarrow\sim q$$ is the symbolic notation for:

Accepted Answer

Inverse Statements

Answer

Conditional Statements

Answer

Converse Statements

Answer

Contrapositive Statements

Answer

Biconditional Statements

Question 5

$$p\leftrightarrow q$$ is the symbolic notation for:

Accepted Answer

Biconditional Statements

Answer

Conditional Statements

Answer

Converse Statements

Answer

Inverse Statements

Answer

Contrapositive Statements

Question 6

What does the following symbol represent?

$$\rightarrow$$

Accepted Answer

If, then

Answer

If and only if

Answer

And

Answer

Or

Answer

Therefore

Question 7

What does the following symbol represent?

$$\sim$$

Accepted Answer

Negation

Answer

If, then

Answer

If and only if

Answer

And

Answer

Or

Question 8

What does the following symbol represent?

$$\vee$$

Accepted Answer

Or

Answer

If, then

Answer

Therefore

Answer

And

Answer

Negation

Question 9

What does the following symbol represent?

$$\wedge$$

Accepted Answer

And

Answer

If and only if

Answer

Therefore

Answer

Or

Answer

Negation

Question 10

What does the following symbol represent?

$$\leftrightarrow$$

Accepted Answer

If and only if

Answer

Therefore

Answer

And

Answer

If, then

Answer

Negation

Question 11

What does the following symbol represent?

$$ herefore$$

Accepted Answer

Therefore

Answer

If and only if

Answer

Or

Answer

If, then

Answer

Negation

Question 12

Given: All dogs like to run

Rewrite the above statement as a conditional statement

Accepted Answer

If it is a dog, then it likes to run

Answer

If I like to run, then I am a dog

Answer

If it is a dog, then it will like to chase cats

Answer

All dogs do not like to run

Question 13

Given: Two lines always intersect at a point.

Rewrite the statement above as a conditional statement

Accepted Answer

If two lines intersect, then they intersect at a point

Answer

Two lines do not intersect ever

Answer

If two lines cross at point, then they intersect

Answer

Two lines do not intersect at a point

Question 14

What is the hypothesis of the following conditional statement:

"If two angles are complementary, then both angles must be acute."

Accepted Answer

Two angles are complementary

Answer

Both angles must be acute

Answer

If both angles are acute, then they must be complementary

Answer

If two angles are not complementary, then both angles are not acute

Answer

If two angles are not acute, then both angles cannot be complementary

Question 15

What is the conclusion of the statement:

"If two numbers are prime, then their product is always odd"

Accepted Answer

Their product is always odd

Answer

Two numbers are prime

Answer

If two numbers are not prime, then their product is not always prime

Answer

If two numbers product is always odd, then they are prime

Answer

If two numbers product is not always odd, then they are not prime

Question 16

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 17

Given: "If two angles form a linear pair, then their sum is 180 degrees"

What is the inverse?

Accepted Answer

If two angles are do not form a linear pair, then their sum is not 180 degrees

Answer

If two angles have a sum of 180 degrees, then they form a linear pair

Answer

If two angles sum is not 180 degrees, then they do not form a linear pair

Answer

Two angles form a linear pair if and only if their sum is 180 degrees

Question 18

"If two angles are adjacent, then they share a side"

What is the contrapositive to the above conditional statement?

Accepted Answer

If two angles do not share a side, then they are not adjacent

Answer

If two angles are not adjacent, then they do not share a side

Answer

If two angles are not adjacent, then they do not share a side

Answer

Two angles are adjacent if and only if they share a side

Question 19

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

Conditional

Answer

Inverse

Answer

Contrapositive

Answer

Biconditional

Question 20

Statement 1: If Emily is not late to class, then she will not be marked tardy.

Statement 2: If Emily is late to class, then she will be marked tardy.

Statement 2 is the ______________ to Statement 1

Accepted Answer

Inverse

Answer

Conditional

Answer

Converse

Answer

Contrapositive

Answer

Biconditional

Question 21

Original: If Willow wants a toy, then she will bark.

What is the following statement in regards to the original?

If Willow does not bark, then she does not want a toy

Accepted Answer

Contrapositive

Answer

Conditional

Answer

Converse

Answer

Inverse

Answer

Biconditional

Question 22

"If two sides of a triangle are congruent, then the angles opposite those sides are congruent."

Which statement is written a biconditional?

Accepted Answer

Two angles of a triangle are congruent if and only if the sides opposite those angles are congruent.

Answer

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

Answer

Two sides of a triangle are congruent and the angles opposite those sides are congruent.

Answer

Two sides of a triangle are not congruent or the angles opposite those sides are not congruent.

Question 23

For a biconditional statement to be valid, which statements must be true?

Select All

Accepted Answer

Conditional

Accepted Answer

Converse

Answer

Inverse

Answer

Contrapositive

Answer

Biconditional

Question 24

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

"If there is lightning, then there is thunder."

Accepted Answer

There is lightning if and only if there is thunder.

Answer

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

Answer

If there is thunder, then there is lightning.

Answer

There is no biconditional statement.

Question 25

Which of the following is a counterexample to the following statement:

All dogs are German Shepherds

Accepted Answer

Corgi

Answer

Rabbit

Answer

Frog

Answer

Fish

Question 26

What is a counterexample to the following:

Every prime number is an odd number.

Accepted Answer

2

Answer

8

Answer

16

Answer

12

Question 27

What is a counterexample to the following:

All equations have integer solutions

Accepted Answer

3x+4=11

Answer

2x-8=12

Answer

5x+12=37

Answer

10x-14=96

Question 28

Given: k: Oatmeal is cereal and m: Massachusetts is a city

Translate the following:

$$\sim k\wedge m$$

Accepted Answer

Oatmeal is not cereal and Massachusetts is a city

Answer

If oatmeal is not cereal, then Massachusetts is a city.

Answer

Oatmeal is not cereal or Massachusetts is a city

Answer

Oatmeal is not cereal if and only if Massachusetts is a city

Question 29

Given: k: Oatmeal is cereal and m: Massachusetts is a city

Translate the following:

$$m\leftrightarrow k$$

Accepted Answer

Massachusetts is a city if and only if oatmeal is a cereal

Answer

Massachusetts is a city and oatmeal is a cereal

Answer

Massachusetts is a city or oatmeal is a cereal

Answer

If Massachusetts is a city, then oatmeal is a cereal

Question 30

Given: p: A quadrilateral is a square and q: it has four sides

Translate the following:

If it does not have four sides or a quadrilateral is not a square

Accepted Answer

$$\sim q\vee\sim p$$

Answer

$$\sim q\wedge\sim p$$

Answer

$$\sim q\rightarrow\sim p$$

Answer

$$ herefore\sim q$$

Question 31

Given: a: Christmas is in December and b: January has 31 days

Translate the following using logic symbols:

Therefore, Christmas is not in December if and only if January has 31 days

Accepted Answer

$$ herefore\sim a\leftrightarrow b$$

Answer

$$b\leftrightarrow\sim a$$

Answer

$$ herefore a ightarrow b$$

Answer

$$\sim a\leftrightarrow b$$

Question 32

Given: p: A cat is an animal, q: A poodle is a cat and r: His cat is gray

Translate the following using logical symbols:

If a cat is an animal and a poodle is not a cat, then his cat is not gray

Accepted Answer

$$\left(p\wedge\sim q\right)\rightarrow\sim r$$

Answer

$$\left(p\vee\sim q\right)\rightarrow\sim r$$

Answer

$$\left(\sim p\wedge\sim r\right)\rightarrow q$$

Answer

$$\left(\sim p\vee\sim r\right)\rightarrow q$$

Question 33

What is the symbolic notation for the Law of Detachment?

Accepted Answer

$$p ightarrow q$$

$$p$$

$$ herefore q$$

Answer

$$p ightarrow q$$

$$\sim q$$

$$ herefore\sim p$$

Answer

$$p ightarrow q$$

$$q ightarrow r$$

$$ herefore p\longrightarrow r$$

Answer

$$p ightarrow q$$

$$\sim p$$

$$ herefore\sim q$$

Question 34

What is the symbolic notation for the Law of Contrapositive?

Accepted Answer

$$p ightarrow q$$

$$\sim q$$

$$ herefore\sim p$$

Answer

$$p ightarrow q$$

$$p$$

$$ herefore q$$

Answer

$$p ightarrow q$$

$$q ightarrow r$$

$$ herefore p\longrightarrow r$$

Answer

$$p ightarrow q$$

$$\sim p$$

$$ herefore\sim q$$

Question 35

What is the symbolic notation for the Law of Syllogism?

Accepted Answer

$$p ightarrow q$$

$$q ightarrow r$$

$$ herefore p\longrightarrow r$$

Answer

$$p ightarrow q$$

$$p$$

$$ herefore q$$

Answer

$$p ightarrow q$$

$$\sim q$$

$$ herefore\sim p$$

Answer

$$p ightarrow q$$

$$\sim p$$

$$ herefore\sim q$$

Question 36

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.

Accepted Answer

If Tom goes fishing then he catches a fish.

Answer

If Tom brings his pole then he goes fishing

Answer

If Tom catches a fish then he brought his pole.

Answer

Tom catches fish

Question 37

Using the law of detachment, what conclusion can be made from the following:

"If you pass this test, then my teacher will be proud of you!"

You made an 88 on the test.

_______________________________________

Accepted Answer

Your teacher will be proud of you.

Answer

You studied!

Answer

If you made an 88, then your teacher is proud of you.

Answer

Your teacher is NOT proud of you.

Question 38

Using the Law of Contrapositive, what is a valid conclusion given:

If this wind keeps up, then we will lose some trees.

We did not lose some trees.

_________________________________

Accepted Answer

The wind did not keep up

Answer

If we did not lose some trees, then the wind did not keep up

Answer

The wind kept up

Answer

Invalid

Question 39

Determine a valid conclusion from the statements:

If a person is a librarian, then they read books

If a person is a friend of Mercedes, then they read books

___________________________

Accepted Answer

Invalid

Answer

If a person is a librarian, then they like to read books

Answer

If they are not a librarian, then they do not like to read books

Answer

Mercedes has a lot of friends

Question 40

What is a valid conclusion given the following statements:

If I miss my bus, then I will be late for school.

I missed my bus.

_________________________________

Accepted Answer

I will be late for school

Answer

I will not be late for school

Answer

If I am late for school, then I missed my bus

Answer

Invalid.

Question 41

"If my mother lets me go to the movies, then I will be happy

I am not happy"

_________________________________________

What is a valid conclusion to the statements above?

Accepted Answer

My mother did not let me go to the movies

Answer

My mother let me go to the movies

Answer

If I am not happy then I was not allowed to go to the movies

Answer

Invalid

Question 42

What is a valid conclusion to the following statements?

"If a quadrilateral is a square, then it has four congruent sides.

Quadrilateral ABCD has four congruent sides.

__________________________________________"

Accepted Answer

Invalid

Answer

Quadrilateral ABCD is a square

Answer

Quadrilateral ABCD is not a square

Answer

If Quadrilateral ABCD has four congruent sides, then it is a square

Question 43

Determine which Law of Logic is represent with the statements below:

"If I go to the movies, then I will eat popcorn.

If I eat popcorn, then I'll enjoy the movie.

If I go the movies, then I'll enjoy the movie"

Accepted Answer

Law of Syllogism

Answer

Law of Detachment

Answer

Law of Contrapositive

Answer

Invalid

Question 44

Determine which Law of Logic is represent with the statements below:

"If an animal is a pig, then it is a mammal.

Leon is a pig.

Therefore, Leon is a mammal."

Accepted Answer

Law of Detachment

Answer

Law of Contrapositive

Answer

Law of Syllogism

Answer

Invalid

Question 45

Determine which Law of Logic is represent with the statements below:

"If a man is wealthy, then he will buy a mansion.

Jacob is not wealthy.

Therefore, Jacob will not buy a mansion."

Accepted Answer

Invalid

Answer

Law of Detachment

Answer

Law of Contrapositive

Answer

Law of Syllogism

Question 46

Determine which Law of Logic is represent with the statements below:

"If you are an accountant, then you enjoy Math.

Greg does not enjoy Math.

Greg is not an accountant."

Accepted Answer

Law of Contrapositive

Answer

Law of Detachment

Answer

Law of Syllogism

Answer

Invalid

Unit 2: Logic Review

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