Title: conditional statements
Course: quiz duplicate error

Q: Write the statement in if-then form.

A counterexample invalidates a statement.
- If it invalidates the statement, then there is a counterexample. (The format of if-then form is “If hypothesis, then conclusion.”)
- If there is a counterexample, then it invalidates the statement. (The format of if-then form is “If hypothesis, then conclusion.”)
- If it is true, then there is a counterexample. (The format of if-then form is “If hypothesis, then conclusion.”)
- If there is a counterexample, then it is true. (The format of if-then form is “If hypothesis, then conclusion.”)
A: If there is a counterexample, then it invalidates the statement.

Q: Write the statement in if-then form.

Spiders can walk on walls.
- If it can walk on walls, then it can walk on walls. (The format of if-then form is “If hypothesis, then conclusion.”)
- If it is a spider, then it can walk on walls. (The format of if-then form is “If hypothesis, then conclusion.”)
- If it is a spider, then it is a spider. (The format of if-then form is “If hypothesis, then conclusion.”)
- If it can walk on walls, then it is a spider. (The format of if-then form is “If hypothesis, then conclusion.”)
A: If it is a spider, then it can walk on walls.

Q: Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counterexample.

If you have a dog, then you are a pet owner.
- If you are a pet owner, then you have a dog. True (The converse of a conditional statement [Image] exchanges the hypothesis and conclusion of the conditional. It is also known as [Image].)
- A dog owner owns a pet. True (The converse of a conditional statement [Image] exchanges the hypothesis and conclusion of the conditional. It is also known as [Image].)
- If you are a pet owner, then you have a dog. False; you could own a hamster. (The converse of a conditional statement [Image] exchanges the hypothesis and conclusion of the conditional. It is also known as [Image].)
- If you have a dog, then you are a pet owner. True (The converse of a conditional statement [Image] exchanges the hypothesis and conclusion of the conditional. It is also known as [Image].)
A: If you are a pet owner, then you have a dog. False; you could own a hamster.

Q: Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counterexample.

All Jack Russells are terriers.
- If a dog is a terrier, then it is a Jack Russell. False; it could be a Scottish terrier. (The converse of a conditional statement [Image] exchanges the hypothesis and conclusion of the conditional. It is also known as [Image].)
- If it is a Jack Russell, then a dog is a terrier. True (The converse of a conditional statement [Image] exchanges the hypothesis and conclusion of the conditional. It is also known as [Image].)
- If a dog is a terrier, then a dog is a terrier. True (The converse of a conditional statement [Image] exchanges the hypothesis and conclusion of the conditional. It is also known as [Image].)
- All Jack Russells are terriers. True (The converse of a conditional statement [Image] exchanges the hypothesis and conclusion of the conditional. It is also known as [Image].)
A: If a dog is a terrier, then it is a Jack Russell. False; it could be a Scottish terrier.

Q: Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample.

People who live in Texas live in the United States.
- People who do not live in the United States do not live in Texas. True (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
- People who do not live in Texas do not live in the United States. False; they could live in Oklahoma. (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
- People who live in the United States live in Texas. False; they could live in Oklahoma. (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
- People who do not live in Texas live in the United States. True (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
A: People who do not live in Texas do not live in the United States. False; they could live in Oklahoma.

Q: Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample.

All quadrilaterals are four-sided figures.
- All non-quadrilaterals are four-sided figures. False; a triangle is a non-quadrilateral. (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
- All four-sided figures are quadrilaterals. True (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
- No quadrilaterals are not four-sided figures. True (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
- No four-sided figures are not quadrilaterals. True (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
A: No quadrilaterals are not four-sided figures. True

Q: Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample.

An equilateral triangle has three congruent sides.
- A non-equilateral triangle has three congruent sides. False; an isosceles triangle has two congruent sides. (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
- A figure that has three non-congruent sides is not an equilateral triangle. True (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
- A non-equilateral triangle does not have three congruent sides. True (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
- A figure with three congruent sides is an equilateral triangle. True (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
A: A non-equilateral triangle does not have three congruent sides. True

Q: Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample.

All country names are capitalized words.
- All capitalized words are country names. False; the first word in the sentence is capitalized. (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
- All non-capitalized words are not country names. True (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
- All non-country names are capitalized words. False; most of the words in the sentence are non-capitalized words. (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
- All non-country names are non-capitalized words. False; the first word in the sentence is capitalized. (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
A: All non-country names are non-capitalized words. False; the first word in the sentence is capitalized.

Q: Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample.

Independence Day in the United States is July 4.
- July 4 is not Independence Day in the United States. False; it is Independence Day. (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
- Non-Independence Day in the United States is not July 4. True (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
- Non-Independence Day in the United States is July 4. False; July 4 is Independence Day in the United States. (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
- Non-July 4 is not Independence Day in the United States. True (The inverse is negating both the hypothesis and conclusion of the conditional. [Image])
A: Non-Independence Day in the United States is not July 4. True

Q: Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample.

If you are 16 years old, then you are a teenager.
- If you are not a teenager, then you are not 16 years old. True (In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
- If you are not 16 years old, then you are not a teenager. False; you could be 17 years old. (In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
- If you are not a teenager, then you are 16 years old. True (In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
- If you are a teenager, then you are 16 years old. False; you could be 17 years old. (In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
A: If you are not a teenager, then you are not 16 years old. True

Q: Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample.

A converse statement is formed by exchanging the hypothesis and conclusion of the conditional.
- A non-converse statement is not formed by exchanging the hypothesis and conclusion of the conditional. True (In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
- A statement not formed by exchanging the hypothesis and conclusion of the conditional is a converse statement. False; an inverse statement is not formed by exchanging the hypothesis and conclusion of the conditional. (In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
- A non-converse statement is formed by exchanging the hypothesis and conclusion of the conditional. False; an inverse statement is formed by negating both the hypothesis and conclusion of the conditional. (In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
- A statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement. True (In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
A: A statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement. True

Q: Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample.

Two angles measuring 180 are supplementary.
- Two angles not measuring 180 are not supplementary. True (In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
- More than two angles measuring 180 are non-supplementary. True (In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
- Non-supplementary angles are not two angles measuring 180. True (In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
- Non-supplementary angles are two angles measuring 180. False; supplementary angles must measure 180. (In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
A: Non-supplementary angles are not two angles measuring 180. True

Q: Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample.

If you have a gerbil, then you are a pet owner.
- If you are not a pet owner, then you do not have a gerbil. True (In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
- If you do not have a gerbil, then you are not a pet owner. False; you could have a dog. (In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
- If you are not a pet owner, then you have a gerbil. False; if you are not a pet owner then you have no pets. (In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
- If you are not a gerbil, then you are not a pet owner. True (In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
A: If you are not a pet owner, then you do not have a gerbil. True

Q: Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample.

Thanksgiving Day in the United States is November 25.
- If it is not November 25, it is Thanksgiving Day in the United States. True (Based on logic rather than general knowledge. In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
- If it is not Thanksgiving Day in the United States, it is not November 25. False; Thanksgiving Day could be another date in a different year so November 25 could be not Thanksgiving Day. (Based on logic rather than general knowledge. In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
- If it is not November 25, it is not Thanksgiving Day in the United States. True (Based on logic rather than general knowledge. In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
- If it is not November 25, it is not Thanksgiving Day in the United States. False; Thanksgiving Day could be another date in a different year. (Based on logic rather than general knowledge. In the contrapositive you negate both the hypothesis and conclusion of the converse statement. [Image])
A: If it is not November 25, it is not Thanksgiving Day in the United States. True

Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample.

The segment bisector is the midpoint.

Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample.

If it is a spider, then it can walk on walls.

Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample.

Two angles measuring 90° are complementary.

Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample.

A conditional statement is formed by a given hypothesis and conclusion.

Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample.

A line is made up of points.

Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample.

A counterexample invalidates a statement.

Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample.

Vertical angles are two nonadjacent angles formed by two intersecting lines.

Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample.

If you buy one can of soup, then you get the second one free.

Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample.

A line is determined by two points.

Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample.

Two segments having the same measure are congruent.