Show that the relation R in the set 4={1,2,3,4,5) given by R={(a,b): |a-bis even} is an...

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Show that the relation R in the set 4={1,2,3,4,5) given by R={(a,b): |a-bis even} is an equivalence relation. Show that all the elements of {1,3,5} are related to each other and all the elements of {2,4} are related to each other. But no element of {1,3,5} is related to any element of {2,4}. Show that the relation R in the set 4={1,2,3,4,5) given by R={(a,b): |a-bis even} is an equivalence relation. Show that all the elements of {1,3,5} are related to each other and all the elements of {2,4} are related to each other. But no element of {1,3,5} is related to any element of {2,4}.

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