Question

The set of all odd integers with respect to addition is_​

Answer 1

For an algebraic structure <G,*> to be a group, it has to satisfy four properties for all a,b,c belonging to G:

Closure: a*b belongs to G

Associativity: (a*b)*c=a*(b*c)

Existence of Identity: There exists e belonging to G such that a*e=e*a=a

Existence of Inverse: There exists k such that a*k=k*a=e

Now, as Varun Tripathi mentioned closure is not satisfied by the set of odd integers.

This is enough to conclude that the set is not a group under addition. But we can go further ahead and say that the identity of integers under addition, 0, does not belong to the set of odd integers as 0 is even. This also helps us to conclude that the algebraic structure is not a group