Let be the statement '' and be the statement ' or '. 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
- Step 1: If , then one of the factors is zero, so .
- Step 2: If or then , so . The conditions are equivalent.
Answer
is both a necessary and a sufficient condition for .
Why not the others: There is no pair for which one statement holds and the other does not, so neither direction can fail.
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