Prove the statement if a and b are integers one number apart then the sum a, b is even using a. Direct proof b. Proof by contradiction
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Answer:
Suppose,
a = 2 × X
b = 2 × Y
where X and Y are any integers that may be even or odd. Multiplying any number by 2 is always even so 2X and 2Y are even.
a + b = 2 × X + 2 × Y = 2 × (X + Y)
The result has a factor of 2. So, it is always even.
Example:
Input: a = 2, b = 4
Output: a + b = 2 + 4 = 6 = 2 × 3
Hence, it is even.
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