Let be the statement ' and ' and be the statement ' and '. Which of the following is correct? (Here and are real numbers.)

Answer and explanation

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

  1. Step 1: If then both and are positive, so .
  2. Step 2: If then and have the same sign, and makes that sign positive, so .
Answer
is both a necessary and a sufficient condition for .
Why not the others: alone would allow two negatives, but the additional condition removes that case.

Practise more Necessary and sufficient conditions.

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