If a and b are two odd positive integers such that a > b, then prove that one of the two numbers $\frac{a + b}{2} a n d \frac{a - b}{2}$ is odd and the other is even.

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\frac{a + b}{2}

\frac{a - b}{2}

\frac{a + b}{2}

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If a and b are two odd positive integer , then prove that one of two numbers $\frac{a + b}{2}$ and $\frac{a - b}{2}$ is odd and other is even.

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If a and b are two odd positive integers such that a > b, then prove that one of the two numbers a+b2 and a−b2 is odd and the other is even.