Let be the statement ' is divisible by 4' and be the statement ' is even'. Which of the following is correct? (Here is an integer.)

Answer and explanation

Correct answer: C. is both a necessary and a sufficient condition for

  1. Step 1: If then is divisible by , so .
  2. Step 2: If were odd then would be odd and not divisible by , so by contraposition. The statements are equivalent.
Answer
is both a necessary and a sufficient condition for .
Why not the others: Neither direction has a counterexample.

Practise more Necessary and sufficient conditions.

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