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

Answer and explanation

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

  1. Step 1: means , i.e. . Every such has , so .
  2. Step 2: But has while , so .
Answer
is a necessary but not a sufficient condition for .
Why not the others: is necessary for since lies inside , but it is not sufficient because of the negative values.

Practise more Necessary and sufficient conditions.

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