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Write whether every positive integer can be of the form $4q + 2$, where $q$ is an integer. Justify your answer.
The given positive integer is $q$.
To do :
We have to find whether every positive integer can be of the form $4q + 2$, where $q$ is an integer.
By Euclid\'s division lemma,
If a and b are two positive integers, then,
$a = b q + r$, where $0 \leq r < b$
Here, $b$ is any positive integer
$a = 4, b = 4q + r$ for $0 \leq r < b$ [$r = 0,1,2, 3$]
This must be in the form $4q, 4q + 1, 4q + 2$ or $4q + 3$.
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