If A = {1, 2, 3, 4}, define relations on A which have properties of being
(i) reflexive, transitive but not symmetric.
(ii) symmetric but neither reflexive nor transitive.
(iii) reflexive, symmetric and transitive.

Explanation

(i) A relation R on set A will be reflexive if `(1, 1) in R, (2, 2) in R, (3, 3) in R, (4,4) in R`
will be transitive if
`(1, 2) in R and (2, 1) in R rArr (1, 1) in R`
`(1, 2) in R and (2, 3) in R rArr (1, 3) in R`
`:. R {{1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1), (2, 3), (1, 3)}`
is reflexive and transitive but not symmetric. Ans.
(ii) A relation R on set A will be symmetric if : `(1, 2)in R rArr (2, 1) in R `
`(2, 3)in R rArr (3, 2) in R`
`:. R = {(1, 2), (2, 1), (2, 3), (3, 2) ,(1, 1), (2, 2), (1, 3)}` is symmetric and transitive but not reflexive . Ans.
(iii) R = {(1.2),(2,2),(3,3), (,4,4) , (1,2), (2,2), (2,3) ,(3,2)}` is reflexive and symmetic but not transitive. Ans.