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If $$k$$ is an integer then which of the following is true?
$$4k + 1 = 2(2k + 1) - 1$$ and $$4k + 3 = 2(2k + 1) + 1$$, so every number of these forms is odd and can be written as $$2m - 1$$ or $$2m + 1$$. But not every odd number is $$4k + 1$$ (for example 3) or $$4k + 3$$ (for example 1). Hence options a and b are correct.
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