Multiple choice general knowledge math & puzzles

"If Tom buys a red skateboard, then Amanda buys green in-line skates." Which statement below is logically equivalent?

  1. If Amanda does not buy green in-line skates, then Tom does not buy a red skateboard.

  2. If Tom does not buy a red skateboard, then Amanda does not buy green in-line skates

  3. If Amanda buys green in-line skates, then Tom buys a red skateboard.

  4. If Tom buys a red skateboard, then Amanda does not buy green in-line skates.
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A Correct answer
Explanation

The contrapositive of 'If P then Q' is 'If not Q then not P,' and these are logically equivalent. Here P is 'Tom buys a red skateboard' and Q is 'Amanda buys green in-line skates.' The contrapositive becomes 'If Amanda does NOT buy green skates (not Q), then Tom does NOT buy a red skateboard (not P)' - option A. Option B is the inverse (not equivalent). Option C is the converse (not equivalent). Option D contradicts the original.

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