Check the relation R={(1,1),(2,2),(3,3),.....,(n,n)} defined on the set S={1,2,3,......n) for the three basic relations.

Show that the relation R in the set {1,2,3} given by R = {(1,1) ,(2,2),(3,3) , (1,2), (2,3)} is reflexive but neither symmetric nor transitive.

Let N be the set of natural numbers and the relation R be defined on N such that R={(x,y): y=2x,x,y in N }. what is the domain codomain and range of R ? Is this relation a functions ?

If A={1,2,3...} and N is the set of natural numbers, then check whether A and N are equal?

Show that the relation R defined in the set A of all triangles as R={(T_(1),T_(2)):T_(1) is similar to T_(2) }, is equivalence relation.

If S_(1), S_(2), S_(3),...,S_(n) are the sums of infinite geometric series, whose first terms are 1, 2, 3,.., n and whose common rations are (1)/(2), (1)/(3), (1)/(4),..., (1)/(n+1) respectively, then find the values of S_(1)^(2) + S_(2)^(2) + S_(3)^(2) + ...+ S_(2n-1)^(2) .