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Question -

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.



Answer -

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

Let qx isan integer and x2 is even.

rx iseven.

To prove that p istrue by contrapositive method, we assume that r is false, andprove that q is also false.

Let x is noteven.

To prove that q isfalse, it has to be proved that x is not an integer or x2 isnot even.

x isnot even implies that x2 is also not even.

Therefore, statement q isfalse.

Thus, the given statement p istrue.

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