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Which of the following statements is/are True?

1. If $x$ and $y$ are two integers whose product is odd, then both must be odd.
2. If $a$ and $b$ are real numbers such that the product ab is an irrational number, then either $a$ or $b$ must be an irrational number.
3. For any integer $m,$ if $m^{2}$ is even, then $m$ is even.
4. The sum of a rational number and an irrational number is irrational.

Assume pow(m,2) is even integer (example 6), then m cannot be an integer.

I do understand that proof by contraposition works here. But why is the example i’ve provided wrong?
m must be given as integer to be precise. Question is edited now.
I think all the options are correct.