Question

Q.1 Prove by contrapositive that if n = a*b, where a and b are positive integers, then

a ≤ √n or b ≤ √n

Answer 1

proof

Assume that both a and b are larger than n^1/2 . Thus, ab>n so that n is not equal to ab. Since the negation of conclusion implies the negation of hypothesis, the original conditional statement is true.