The relation R in the set `{a,b,c}` given by `R={(a,a),(b,b),(a,b),(b,a)}` is

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.

A relation R in S={a,b,c} is defined as R={(a,a),(a,b),(b,b),(c,c)} . which element of relation R be removed to make R an equivalence relation?

Prove that the relation R in the set A={1,2,3,4,5,6,7} given by R={(a,b):|a-b|iseven} is an equivalence relation.

show that R is an equivaence relation R defined on the set S={1,2,3,4,5} given by R={(a,b):|a-b| is even } is an equivalence relation .

Show that the relation R in the set A={x: x in N,x <=10} given by R={(a, b):a+ b is even number] is an equivalence relation. Also find the set of all elements related to 3

Consider the following two binary relations on the set A = {a,b,c}, R_(1) = {(c,a),(b,b), (a,c), (c,c), (b,c),(a,a)} R_(2) ={(a,a),(a,b),(c,c),(b,a),(b,b),(a,c)} , Then:

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

Show that the relation R in the set A={x in N:0<=x<=12 } given by R={ (a,b):|a-b| is a multiple of 4 } is an equivalence relation?