Question

1. choose the best answer.

the negation of the hypothesis and conclusion of a conditional statement results in a related conditional statement called a(n) ______
○ converse
○ negation
○ contrapositive
○ inverse

1. choose the best answer.

the ______ is the negative form of any part of a conditional statement.
○ contrapositive
○ negation
○ inverse
○ converse

Explanation:

Question 16

To solve this, we recall the definitions of related conditional statements:

• Converse: Swaps hypothesis and conclusion (e.g., if \( q \), then \( p \) for "if \( p \), then \( q \)").
• Negation: Denies a statement, not a conditional transformation.
• Contrapositive: Negates and swaps (e.g., if \(

eg q \), then \(
eg p \)).

• Inverse: Negates hypothesis and conclusion (e.g., if \(

eg p \), then \(
eg q \)).

The question describes negating both hypothesis and conclusion, which matches the inverse.

We analyze the options:

• Contrapositive: A transformed conditional (negate and swap), not just a negative form of a part.
• Negation: Defined as the negative form of a statement (or part of one).
• Inverse: Negates both hypothesis and conclusion of a conditional, not just a "part".
• Converse: Swaps hypothesis and conclusion, no negation of a part.

The term for the negative form of any part of a conditional is negation.

Answer:

D. inverse

Question 17