Let R be the relation on the set A = {1, 2, 3, 4, 5, 6, 7} defined by the rule (a,b) eR if the integer (a - b) is divisible by 4. List the elements of R and its inverse? b) Check whether the relation R on the set S = {1, 2, 3} is an equivalent relation where R = {(1,1), (2,2), (3,3), (2,1), (1,2), (2,3), (1,3), (3,1)}. Which of the following properties R has: reflexive, symmetric, anti-symmetric, transitive? Justify your answer in each case? Let S = {a, b, c} and R = {(a,a), (b,b), (c, c), (b, c), (c, b)}, find [a], [b] and [c] (that is the equivalent class of a, b, and c). Hence or otherwise find the set of equivalent class of a, b and c? c)

How many relations are there on the set {a, b}. Show all possible relations on the set {a, b} in matrix format.

Define: what is an equivalence relation?

Determine whether the given relation is an equivalent relation on (1, 2, 3, 4, 5} If the relation is an equivalence relation, list the equivalence classes (x, y E {1,2, 3, 4, 5} . ) 3, 4, 5}. 1. {(1,1), (2, 2) , (3, 3) , (4, 4) , (5, 5) , (1, 3) , (3, 1)} 2. {(x, y) | 3 divides x + y}