Chapter 2 review practice quiz

Which of the following is true about the conditional statement below?

If a man is 7 feet tall, then he plays basketball.

• Hypothesis: a man is 7 feet tall

  Conclusion: he plays basketball

• Hypothesis: IF a man is 7 feet tall

  Conclusion: THEN he plays basketball

• Hypothesis: THEN he plays basketball

  Conclusion: IF a man is 7 feet tall

• Hypothesis: he plays basketball

  Conclusion: a man is 7 feet tall

Answer explanation

The correct choice identifies the hypothesis as 'a man is 7 feet tall' and the conclusion as 'he plays basketball', which accurately reflects the structure of the conditional statement given.

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. 

Answer explanation

The inverse of a conditional statement "If P, then Q" is "If not P, then not Q." Here, P is "I have a Siberian Husky" and Q is "I have a dog." Thus, the correct inverse is "If I do not have a Siberian Husky, then I do not have a dog."

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. 

Answer explanation

The contrapositive of 'If I have a Siberian Husky, then I have a dog' is 'If I do not have a dog, then I do not have a Siberian Husky.' This maintains the logical equivalence of the original statement.

What does this mean?

• Conditional Statement

• Inverse Statement

• Converse Statement

• Contrapositive Statement

Answer explanation

An Inverse Statement negates both the hypothesis and conclusion of a conditional statement. If the original statement is 'If P, then Q', the inverse is 'If not P, then not Q'. This matches the correct answer.

What does this mean?

• Conditional Statement

• Converse

• Inverse

• Contrapositive

Answer explanation

The contrapositive of a conditional statement reverses and negates both the hypothesis and conclusion. It is logically equivalent to the original statement, making it the correct choice here.

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.

Answer explanation

In the statement "If I have a Siberian Husky, then I have a dog," the hypothesis is the part that follows 'if.' Therefore, the correct choice is "I have a Siberian Husky."

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

• If I have a Siberian Husky.

• I have a Siberian Husky.

• Then I have a dog.

• I have a dog.

Answer explanation

The statement "If I have a Siberian Husky, then I have a dog" indicates that having a Siberian Husky leads to the conclusion that I have a dog. Therefore, the correct conclusion is "I have a dog."

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.

Answer explanation

The converse of a statement reverses the hypothesis and conclusion. Here, the original statement is 'If angles are congruent, then the measures of the angles are equal.' The converse is 'If the measures of the angles are equal, then the angles are congruent.'

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.

Answer explanation

The inverse of a conditional statement "If P, then Q" is "If not P, then not Q." Here, the original statement is "If angles are congruent (P), then the measures of the angles are equal (Q)." Thus, the inverse is "If angles are not congruent, then the measures of the angles are not equal."

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.

Answer explanation

The contrapositive of a statement "If P, then Q" is "If not Q, then not P." Here, "If angles are not congruent (not P), then the measures of the angles are not equal (not Q)" is the correct choice.