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Examine the statements below: p: x and y are integers, and both are odd. q: the product xy is odd. Which of the following is correct?

1. p implies q is true
2. not q implies p is true
3. Both (a) and (b)
4. Neither (a) nor (b)

Correct answer: p implies q is true

Solution

If x,y are both odd then xy is odd, so p => q is true. But ~q (xy even) does not imply p (both odd) - e.g. x=2,y=3 gives xy even yet p false. Hence only statement (a) holds.

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