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Let R be the realtion defined in the set...

Let R be the realtion defined in 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}.`

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