Equivalence classes

Let L be the set of lines in XY plane. Define a relation s in L by xSy x = y or x-Ly or x Il y. Is S an equivalence relation? If so, what are equivalence classes ? What is the equivalence class containing X-axis ? What happens if L is the set of all lines in space?

Show that the relation R in the set A={1,2,3,4,5} given by R={(a,b):|a b | is divisible by 2} is an equivalence relation.Write all the quivalence classes of R .

Gram Equivalent || Law OF Equivalence Class Illustrations with Short Tricks

If A ={ 1, 2, 3,. . . , 10} R : A to A R = { (a, b) : | a - b| is a multiple of 3} is an equivalence relation, then the equivalence class [1] is

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 R be the relation in the set Z of integers given by R={(a,b):2 divides a-b}. Show that the relation R transitive ? Write the equivalence class [0].