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Consider the statement: 'If x = 5 and y = -2, then x - 2y = 9.' Which of the following is its contrapositive?

1. If x - 2y != 9, then x != 5 or y != -2
2. If x - 2y != 9, then x != 5 and y != -2
3. If x - 2y = 9, then x = 5 and y = -2
4. None of these

Correct answer: If x - 2y != 9, then x != 5 or y != -2

Solution

The contrapositive negates both parts and reverses them; negating the conjunction gives an 'or', so it reads: if x-2y != 9 then x != 5 or y != -2.

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