If R_1 and R_2 ·are equivalence relations in a set A, show that R_1 nn R_2 is also 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

Let A be the set of all students of class XII in a school and R be the relation, having the same sex on A, and then prove that R is 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.

The smallest equivalence relation R on set A ={1,2,8} is=

If R is the relation in N xx N defined by (a, b) R (c,d) if and only if (a + d) =(b + c), show that R is an equivalence relation.

Show that relation R = {(P_1, P_2) : P_1 and P_2 have same numbers of sides}, defined on the set of all polygons is an equivalence relation

If relation R defined on set A is an equivalence relation, then R is

Let A={x in Z:0 le x le 12} . Show that R={(a,b):a,b in A,|a-b| is divisible by 4} is an equivalence relation. Find the set of all elements related to 1. Also write the equivalence class [2]

On the set N of all natural numbers, a relation R is defined as follows: AA n,m in N , n R m Each of the natural numbers n and m leaves the remainder less than 5.Show that R is an equivalence relation. Also, obtain the pairwise disjoint subsets determined by R.