If `R_1` and `R_2` are equivalence relations in a set A, show that `R_1nnR_2` is also an equivalence relation.

If R is an equivalence relation on a set A, then R^-1 is

Let R_1 and R_2 be equivalence relations on a set A, then R_1uuR_2 may or may not be

The union of two equivalence relations on a set is not necessarily an equivalence relation on the set.

Statement-1: If R is an equivalence relation on a set A, then R^(-1) is also an equivalence relation. Statement-2: R = R^(-1) iff R is a symmetric relation.

Let R and S be two equivalence relations on a set A Then : A. R uu S is an equvalence relation on A B. R nn S is an equirvalenee relation on A C. R - S is an equivalence relation on A D. None of these

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

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 , pandqa r ei n t e g e r ss u c ht h a tn ,q"!="0andq 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

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.

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

Which of one of the following relations on R is equivalence relation