What is the contrapositive of 'If it rains, the field is muddy'?

• A. If the field is not muddy, it did not rain.
• B. If it is not raining, the field is not muddy.
• C. If the field is muddy, it rained.
• D. If it rains, the field is not muddy.

Answer: (A)

The main idea here is how the contrapositive of a conditional works. For a statement of the form If P then Q, the contrapositive is If not Q then not P. It uses the same truth value as the original.

In this case, P is “it rains” and Q is “the field is muddy.” The contrapositive becomes If the field is not muddy, then it did not rain. This directly flips and negates both parts, which is why it is logically equivalent to the original statement.

Why the other forms don’t fit: the inverse would be If it is not raining, the field is not muddy, which is not the contrapositive. The converse would be If the field is muddy, it rained. The remaining option is just the negation of the conclusion in the original, not the contrapositive.