Explanation:
Exp: D
positive odd integer
Let a be a given positive odd integer.
Applying Euclid’s Division Lemma to a and b = 4
\(\text{we have,a+r where0}\leq\text{r<4}\)
\(\Rightarrow\)r = 0, 1, 2, 3
\(\Rightarrow\)a = 4q or 4q + 1 or 4q + 2 or 4q + 3
But a = 4q and 4q + 2 = 2 (2q + 1) are clearly even.
Also a = 4q, 4q + 1, 4q + 2, 4q + 3 are consecutive integers,
therefore any positive odd integer is of the form 4q + 1 and 4q + 3
where q is some integer