Answer :

It is given that the relation R in the set A = {x Z : 0 x 12}, given by

R = {(a, b) : a = b}


For any element a ϵ A, we have (a,a) ϵ R as a = a.


Therefore, R is reflexive.


Now, Let (a,a) ϵ R


a = b


b = a


(b,a) ϵ R


Therefore, R is symmetric.


Now, Let (a,b), (b,c) ϵ R


a = b and b = c


a = c


(a,c) ϵ R


Therefore, R is transitive.


Therefore, R is an equivalence relation.


The set of elements related to 1 will be those elements from set A which are equal to 1.


Therefore, the set of elements related to 1 is {1}.


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