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Consider the statement: if x = 5 and y = −2, then x − 2y = 9. Its contrapositive is:

1. If x−2y ≠ 9, then x ≠ 5 and y ≠ −2
2. If x−2y = 9, then x ≠ 5 and y ≠ −2
3. x−2y = 9 if and only if x = 5 and y = −2
4. None of these

Correct answer: None of these

Solution

Statement: if (x=5 AND y=-2) then x-2y=9. Contrapositive of 'if P then Q' is 'if ~Q then ~P', where ~P = (x!=5 OR y!=-2). So it reads 'If x-2y!=9, then x!=5 OR y!=-2'. The listed option uses AND instead of OR, so none of the options match -> None of these.

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