Question

Define a relation R on the set {1, 2, 3, 4} as follows: T = {(1, 4),(2, 3),(2, 4),(4, 1),(2, 1),(1, 2),(3, 2)}

Answer 1

only symmetric

Explanation:

Given is a relation R on the set

{1, 2, 3, 4} as follows: T = {(1, 4),(2, 3),(2, 4),(4, 1),(2, 1),(1, 2),(3, 2)}

To check whether reflexive, symmetric or transitive

a) It is not reflexive as (1,1) is not in T

b) It is symmetric because for every (x,y) we get (y,x)

c) Not transitive because counter example is (1,4) (4,1) did not imply (1,1)