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Show that the following statement is tru...

Show that the following statement is true by the method of contrapositive. P: If x is an integer and `x^(2)` is even, then x is also even.

Text Solution

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Let x is not even.
`because x=2n+1rArrx^2=(2n+1)^2=4n^2+4n+1=4(n^2+n)+1`
which is odd.
`rArr x^2` is odd.
Therefore, 'if q is not true, then p is not true 'is proved.
`rArr` Given statement is true.
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