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Question: The statement, " If the square of an integer is even, then the integer is even", is:


A ) False
B ) True

Steps to derive

1 Let a2 be an even integer and assume that a is odd.

2 Then a = 2 n + 1

3 a2 = (2 n + 1)2
 [Square each side of the equation.]

4 a2 = 4 n2 + 4 n + 1
 [Use formula (x + y)2 = x2 + 2xy + y2.]

5 a2 = 2 (2 n2 + 2 n) + 1

6 This implies that a2 is odd, which contradicts our assumption that a2 is an even integer.

7 So, a is an even integer.

8 Therefore, the statement "if the square of an integer is even, then the integer is even ", is true.



Hence the right answer is Option B

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