'Let `R` be the relation defined on the set `A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7}` by `R={(a ,\ b):`

"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}."