Define p on z by for m,n`in` z, mpn if and only if `mn>=0`. Check whether p is an equivalence relation on z.

The ralation R on Z is defined by for m, nin Z , mRnimpliesm/n is a power of 2. Examine whether it is an equivalence relation.

Let R={(m,n):2 divides m+n} on Z. Show that R is an equivalence relation on Z.

Let n be a fixed positive integer. Define a relation R on Z as follows for all a, b in Z, aRb, if and only if a-bis divisible by n. Show that R is an equivalence relation.

A relation R on the set of complex numbers is defined by z_1 R z_2 if and only if (z_1-z_2)/(z_1+z_2) is real Show that R is an equivalence relation.

Let Z be the set of all integers. A relation R is defined on Z by xRy to mean x-y is divisible by 5. Show that R is an equivalence relation on Z.

Let Z be the set of all integers. A relation R is defined on Z by xRy to mean x-y is divisible by 5. Show that R is an equivalence relation on Z.

Let Z be the set of all integers. A relation R is defined on Z by xRy to mean x-y is divisible by 5. Show that R is an equivalence relation on Z.

Which of the following defined on Z is not an equivalence relation ?

A relation R on the set of complex numbers is defined by z_1 R z_2 if and oly if (z_1-z_2)/(z_1+z_2) is real Show that R is an equivalence relation.

A relation R is defined on the set of integers Z Z as follows R= {(x,y) :x,y inZ Z and (x-y) is even } show that R is an equivalence relation on Z Z .