The inverse of an equivalence relation is an equvalence 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 union of two equivalence relations is an equivalence relation.

Define 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.

What is an equivalence relation? Show that the relation of'similarity' on the set S of all triangle in a plane is an equivalence relation.

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

Show that the relation is congruent to on the set of all triangles in a plane is an equivalence relation

If the relation R in a set of integers defined as R = {(a, b): (a + b) is divisible by 7}, is an equivalence relation, then the equivalence class containing 0 is:

Let M be the set of men and R is a relation is son of defined on M.Then,R is ( a) an equivalence relation (b) a symmetric relation (c) a transitive relation (d) None of these

Let M be the set of men and R is a relation 'is son of defined on M.Then,R is (a) an equivalence relation (b) a symmetric relation only (c) a transitive relation only (d) None of the above