Show that the relation `~` on `ZZ-{0}timesZZ-{0}` defined by `(m,n)~(p,q)Leftrightarrowmq=np` is an equivalence relation.

Show that the relation R on Z – {0} defined by R={(m,n)|frac[m][n] is power of 5} is an equivalence relation.

Prove that the relation R on the set Z of all integers defined by R={(a, b):a-b is divisible by n} is an equivalence relation.

Let ~ be defined by (m,n)~(p,q) if mq=np where m, n, p, qinZ -{0}. Show that it is an equivalence relation.

Show that the relation R on the set Z of integers given by R = {(a,b): 2 divides (a - b)} is an equivalence relation.

Show that the relation R on the set A = {1,2,3,4,5) given by R = {(a,b): la -bl is even)} is an equivalence relation. Also, show that all elements of (1, 3, 5) are related to each other and all the elements of (2, 4) are related to each other, but no element of (1, 3, 5) is related to any element of (2, 4).

Show that the relation R on the set A={1, 2, 3, 4, 5} given by R={(a,b): abs(a-b) is even} in an equivalence ralation.

Let R be the relation on Z defined by aRb iff a-b is an even integer. Show that R is an equivalence relation.

If N denotes the set of all natural numbers and R be the relation on N xx N defined by (a, b) R (c, d) if ad(b+ c)=bc(a+d) . Show that R is an equivalence relation.

Show that the relation S defined on set N xx N by (a, b) S(c,d) rArr a+d=b+c is an equivalence relation.