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


A ) False
B ) True

Steps to derive

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

2 Then a = 2 n

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

4 a2 = 4n2

5 a2 = 2 (2n2)

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

7 So, a is an odd integer.

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



Hence the right answer is Option B

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