Let be the statement ' is even' and be the statement ' and are both even'. Which of the following is correct? (Here and are integers.)

Answer and explanation

Correct answer: D. is a necessary but not a sufficient condition for

  1. Step 1: If and are both even then is even, so : is necessary for .
  2. Step 2: But , gives an even sum without both being even, so .
Answer
is a necessary but not a sufficient condition for .
Why not the others: Two odd numbers also have an even sum, so the condition is not sufficient.

Practise more Necessary and sufficient conditions.

Free questions with an explanation for every one, and full timed TMUA mock tests.