Question: b) Let A = {1, 2, 3, 4} and let R = { (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 4),

b) Let A = {1, 2, 3, 4} and let R = { (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 4), (3, 1), (3, 3), (4, 1), (4, 4) }. A) Not Reflexive as (1,1), (2,2), (3,3), (4,4), don't belong to R Irreflexive as (1,1),(2,2), (3,3),(4,4), all don't belong to R Not Symmetric as for (2,3),(3,2) doesn't belong to R Asymmetric as (2,3) belong to R and (3,2) doesn't. Also there is no (1,1), (2,2), (3,3) or (4,4) and (3,2) doesn't Antisymmetric as (2,3) belong to R Transitive as to prove not transitive, we need to have (a,b), (b,c) = R and (a,c) doesn't equal R. but there is no counter example. B) Reflexive as all (1,1), (2,2), (3,3),(4,4) belong to R Not Reflexive as all (1,1), (2,2),(3,3), (4,4) belong to R Not Symmetric as (2,4) belongs to R, but (4,2) does not belong to R Not Asymmetric as both (1,2) belong to R and (2,1) belongs to R. Also (1,1) ,(2,2), (3,3) (4,4) belongs to R Not Antisymmetric as(1,2) belongs to R and (2,1) belongs to R Not Transitive as (1,2) belongs to R , (2,4) belongs to R but (1,4) doesn't belong to R

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