Let A={1 , 2, 3, 4,5, 6} and let `S=P(A)`, the power set of A How many equivalence classes are there ? List one element from each equivalence class

Write the equivalence class [3]_7 as a set.

Congruence modulo 3 relation partitions the set Z into how many equivalence classes ?

Let A ={1,2,3} be a given set. Define a relation on A which is an equivalence relation on A

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 equivalence classes of R .

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

Let A ={1,2,3,4,5,6}, then total number of elements of the set A xxA is-

Let A={1,2,3},\ B={4,5,6,7} and let f={(1,4),\ (2,5),\ (3,6)} be a function from A to B . State whether f is one-one or not.

Let A = {1, 2, 3}, B { 4, 5, 6} and let f = {(1,4),(2,5)(3,6)} be a function from A to B. Show that f is one-one.