Show that the relation `R={(a,b):aleb}` is not equivalence relation

Show that each of the relation R in the set A = {x in Z : 0 le x le 12} , given by: R = {(a, b) : a = b} , is an equivalence relation. Find the set of all elements related to 1 in each case.

Which one of the following relations on RR is an equivalence relation ?

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

Statement-1: The relation R on the set N xx N defined by (a, b) R (c, d) iff a+d = b+c for all a, b, c, d in N is an equivalence relation. Statement-2: The intersection of two equivalence relations on a set A is an equivalence relation.

Consider the following relations: R = {(x, y) | x, y are real numbers and x = wy for some rational number w}; S={(m/n , p/q)"m , n , p and q are integers such that n ,q"!="0 and q m = p n"} . Then (1) neither R nor S is an equivalence relation (2) S is an equivalence relation but R is not an equivalence relation (3) R and S both are equivalence relations (4) R is an equivalence relation but S is not an equivalence relation

Show that the relation R defined by : R = (a,b) : a-b is divisible by 3 a,b in N is an equivalence relation.

Show that the relation R in the set Z of integers given by R = {(a, b) : 2 divides a – b} is an equivalence relation.

Prove that the relation R defined on the set Z of integers as R= {(a, b) : 4 divides abs(a-b)} is an equivalence relation.