Let `R` be the relation defined on the set `A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7}` by `R={(a ,\ b):` both `a` and `b` are either odd or even}. Show that `R` is an equivalence relation. Further, show that all the elements of the subset {1, 3, 5, 7} are related to each other and all the elements of the subset {2, 4, 6} are related to each other, but no element of the subset {1, 3, 5, 7} is related to any element of the subset {2, 4, 6}.

Explanation

We observe the following properties of `R`.



Reflexivity :




Let a be an arbitrary element of `R`. Then,




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