Which of the following is sufficient to show that the statement *'For every real number , ' is false*?

Answer and explanation

Correct answer: B. Exhibiting one real number with

  1. Step 1: A universal statement is disproved by a single case where it fails.
  2. Step 2: For : , so fails. One such number suffices.
Answer
Exhibiting one real number with .
Why not the others: Checking more cases where it holds, or showing it holds for many numbers, can never disprove a universal claim.

Practise more Proof structure.

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