Question

Prove the following statement by contrapositive method If x is an integer and x is even then x is also even.​

Answer 1

Answer:

p : If x is an integer and x

2

is even then x is also even.

Let q : x is an integer and x

2

is even

r : x is even

To prove that p is true by contrapositive method we assume that r is false and prove that q is also false.

Let x is not even

To prove that q is false, it has to be proved that x is not an integer or x

2

is not even.

x is not even implies that x

2

is also not even.

Therefore statement q is false.

Thus the given statement p is true