Consider the relation R on the set 1 2 3 4 5 defined by the

Consider the relation R on the set {1, 2, 3, 4, 5} defined by the rule (x, y) element R if 3 divides x - y List the element of R List the element of R^-1 Is the element of R is reflexive, symmetric, antisymmetric?

Solution

ANSWER :-

1) Elements of R :-

{ (1,1), (2,2) ,(3,3), (4,4), (5,5) , (1,4) (4,1) ,(2,5), (5,2) }.

2) Elements of R^-1

The elements of R^-1 is same as R. R= R^-1

{ (1,1), (2,2) ,(3,3), (4,4), (5,5) , (1,4) (4,1) ,(2,5), (5,2) }.

3)

R IS Reexive,

R IS Symmetric,

R IS NOT antisymmetric.