Prove by CONTRAPOSITIVE Suppose x Z If x26x5 is even then x

Suppose x Z. If x2-6x+5 is even, then x is odd. Prove by contrapositive.

Solution

Contrapositive of this statement is

If x is not od then x^2-6x+5 is not even

Proof.

x is not odd means x is even ie x=2m for some integer , m

x^2-6x+5=(2m)^2-6*2m+5=4m^2-12m+5=2(2m^2-6m+2)+1=odd number

Hence, x^2-6x+5 is not even

HEnce proved