For some Integer q , every odd integer is of the form a: q. , b: q+1 c: 2q , d: none of these ( give full explanation of answer please !!!!
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We know that, odd intergers are 1,3,5,...
So, it can be written in the form of 2q + 1.
where, q = integer = z
or q = ...,-1,0,1,2,3,...
∴ 2q + 1 = ...,-3,-1,1,3,5,...
Alternate method
Let 'a' be the given positive integer .On dividing 'a' by 2, let q be the quotient and r be the remainder. Then, by Euclid's division algorithm, we have
a = 2q + r, where 0 ≤ r < 2
⇒ a = 2q + r, where r = 0 or r = 1
⇒ a = 2q or 2q + 1
when a = 2q + 1 for some integer q, then clearly a is odd.
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