Prove by contrapositive Let abcZ If n not divides ab then n

Prove by contrapositive: Let a,b,cZ. If n not divides ab, then n not divides a and n not divides b

Solution

We have to prove that if ab is not divisible by n then a and b are also not divisible by n.

the contrapositive example can be as follows:

let a 10 and b 7

let n 14.

ab=170 which is is not divisible by 14 but if we take seperately n cannot divide a abd b .

Hence proved by contrapositive