What is the contrapositive of the statement "If it rains, then the ground is wet"?

Question

Accepted Answer

If the ground is not wet, then it did not rain. The contrapositive of a conditional statement "If P, then Q" is "If not Q, then not P." Both the original statement and its contrapositive always have the same truth value - they are logically equivalent. For the given statement, P is "it rains" and Q is "the ground is wet," so the contrapositive is "If the ground is not wet, then it did not rain."

The statement "If the ground is wet, then it rained" is the converse (If Q, then P), which is not logically equivalent to the original; wet ground could have other causes. The statement "If it does not rain, then the ground is not wet" is the inverse (If not P, then not Q), which is also not logically equivalent to the original; sprinklers could wet the ground without rain. The statement "It rains and the ground is not wet" is the negation of the original conditional, not its contrapositive.

Understanding contrapositives, converses, and inverses is essential for the DSST exam. Students must know that a conditional and its contrapositive are logically equivalent, while the converse and inverse are logically equivalent to each other but not necessarily to the original statement.

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