Is the set of even integers a group under addition what abou

Is the set of even integers a group under addition?

what about the set of odd integers? Why or why not?

Yes, because

The set of even integers are {- - - - ,-6,-4,-2, 0,2,4,6, - - - - -}

1) sum of any two even integers is again an even integer

so even integers are closure under addition

2) If a,b,c are any 3 even integers then a+(b+c)=(a+b)+c

so even integers satisfies associative property under addition

3) \'0\' is additive identify in set of even integers under addition

4) for every even integer 2n having inverse even integer \'-2n\' such that 2n+(-2n)=0

therefore set of integers are a group under addition

but set of odd integers are not a group under addition

because sum of any two odd integers is not odd integer

since not having closure it is not a group

there is no exists additive identity also