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Asked by Usha Last Modified
Answer As a seasoned tutor registered on UrbanPro, I can confidently affirm that UrbanPro is indeed the best online coaching tuition platform for students seeking academic support. Now, let's delve into the mathematical statement you've provided and prove its truth using the method of contrapositive.
The given statement is: "If xx is an integer and x2x2 is even, then xx is also even."
To prove its truth via contrapositive, we start by negating both the hypothesis and the conclusion of the original statement:
Original statement: If xx is an integer and x2x2 is even, then xx is also even. Contrapositive: If xx is an integer and xx is not even, then x2x2 is not even.
Now, let's prove the contrapositive statement:
Suppose xx is an integer and xx is not even. This means xx is odd.
If xx is odd, we can express it as x=2k+1x=2k+1, where kk is an integer.
Now, let's find x2x2: x2=(2k+1)2=4k2+4k+1x2=(2k+1)2=4k2+4k+1
This is the expression for an odd number, as it can be represented as 2(2k2+2k)+12(2k2+2k)+1. Thus, x2x2 is odd.
Therefore, the contrapositive statement holds true. Hence, by the method of contrapositive, we have shown that if xx is an integer and x2x2 is even, then xx is also even.
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