Question

Which of the following is the negation of statement “a*b = b*a for every real number a and b”?

(a) a*b ≠ b*a for every real number a and b

(b) a*b = b*a for every real number a or b

(c) There exists real number a and b for which a*b ≠ b*a

(d) There exists real number a and b for which a*b = b*a

I have been asked this question during an interview.

Question is from Mathematical Reasoning topic in chapter Mathematical Reasoning of Mathematics – Class 11

Answer 1

Right choice is (c) There exists real number a and b for which a*b ≠ b*a

For explanation I would say: Negation of for every is not for every. a*b = b*a not for every real number a and b.

This means There exists real number a and b for which a*b ≠ b*a.