Questions: Fill in the blank so that the resulting statement is true. The inverse of p → q is

Solution Steps

To find the inverse of a conditional statement \( p \rightarrow q \), we need to negate both the hypothesis and the conclusion, resulting in \( \neg p \rightarrow \neg q \).

The given conditional statement is \( p \rightarrow q \). This means "if \( p \) is true, then \( q \) is true."

The inverse of a conditional statement \( p \rightarrow q \) is formed by negating both the hypothesis and the conclusion. Thus, the inverse is expressed as \( \neg p \rightarrow \neg q \).

Using the values \( p = \text{True} \) and \( q = \text{False} \):

• The negation of \( p \) is \( \neg p = \text{False} \).
• The negation of \( q \) is \( \neg q = \text{True} \).

Therefore, the inverse statement becomes \( \text{False} \rightarrow \text{True} \).

Final Answer