Consider a proposition given as : "x ≥ 6, if x² ≥ 25" and its proof as :
Consider a proposition given as : "x ≥ 6, if x² ≥ 25" and its proof as :
If x ≥ 6, then x² = x . x ≥ 6 . 6 = 36 ≥ 25
Which of the following is correct w.r.to the given proposition and its proof?
(1) The proof shows the converse of what is to be proved
(2) The proof starts by assuming what is to be shown
(3) The proof is correct and there is nothing wrong
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Correct answer: (C) (1) and (2)
Explanation
The proposition is "if x² ≥ 25 then x ≥ 6", but the proof assumes x ≥ 6 and derives x² ≥ 25. So the proof starts by assuming what is to be shown and actually proves the converse; the proof is not correct. Statements (1) and (2) are correct, statement (3) is not.