Show that the following statement is true by the method of contrapositive.

p: If x is an integer and x2 is even, then x is also even.

Asked by Pragya Singh | 11 months ago |  59

1 Answer

Solution :-

Let p: If x is an integer and x2 is even, then x is also even

Let q: x is an integer and x2 is even

r: x is even

By contrapositive method, to prove that p is true, 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 x2 is not even

x is not even indicates that x2 is also not even.

Hence, statement q is false.

Therefore, the given statement p is true

Answered by Abhisek | 11 months ago

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