Questions: Write the converse, inverse, and contrapositive of the statement in sentence form. If the menu includes onion rings, then I do not stay on my diet. The converse of the given statement is which of the following? A. If the menu does not include onion rings, then I stay on my diet. B. If I do not stay on my diet, then the menu does not include onion rings. C. If I stay on my diet, then the menu does not include onion rings. D. If I do not stay on my diet, then the menu includes onion rings. The inverse of the given statement is which of the following? A. If the menu does not include onion rings, then I stay on my diet. B. If I do not stay on my diet, then the menu does not include onion rings. C. If I stay on my diet, then the menu does not include onion rings. D. If I do not stay on my diet, then the menu includes onion rings.

Solution Steps

To solve this problem, we need to understand the definitions of converse, inverse, and contrapositive for a conditional statement. The original statement is "If the menu includes onion rings, then I do not stay on my diet." The converse is formed by swapping the hypothesis and conclusion. The inverse is formed by negating both the hypothesis and conclusion. The contrapositive is formed by both swapping and negating the hypothesis and conclusion.

The original statement is: "If the menu includes onion rings, then I do not stay on my diet." This is a conditional statement of the form \( p \rightarrow q \), where \( p \) is "the menu includes onion rings" and \( q \) is "I do not stay on my diet."

The converse of a conditional statement \( p \rightarrow q \) is formed by swapping the hypothesis and conclusion, resulting in \( q \rightarrow p \). Therefore, the converse is: "If I do not stay on my diet, then the menu includes onion rings."

The inverse of a conditional statement \( p \rightarrow q \) is formed by negating both the hypothesis and conclusion, resulting in \( \neg p \rightarrow \neg q \). Therefore, the inverse is: "If the menu does not include onion rings, then I stay on my diet."

The contrapositive of a conditional statement \( p \rightarrow q \) is formed by both swapping and negating the hypothesis and conclusion, resulting in \( \neg q \rightarrow \neg p \). Therefore, the contrapositive is: "If I stay on my diet, then the menu does not include onion rings."

Final Answer