Given below are relations on the set S times S, where S = {1, 2, 3, 4}. Choose t

Question

Given below are relations on the set S times S, where S = {1, 2, 3, 4}. Choose the properties of each relation. A. {(2, 2), (2, 3), (2, 4), (3, 2), (3, 3), (3, 4)} symmetric antisymmetric reflexive irreflexive transitive none B. {(1, 1), (1, 2), (2, 1), (2, 2), (3, 3), (4, 4)} symmetric antisymmetric reflexive irreflexive transitive none C.{(2, 4), (4, 2)} symmetric antisymmetric reflexive irreflexive transitive none D. {(1, 2), (2, 3), (3, 4)} symmetric antisymmetric reflexive irreflexive transitive none E. {(1, 1), (2, 2), (3, 3), (4, 4)} symmetric antisymmetric reflexive irreflexive transitive none F.}(1, 1), (1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)} symmetric antisymmetric reflexive irreflexive transitive none

Explanation / Answer

A - Transitive - As per the rule (a, b) R and (b, c) R (a, c) R,

B- (i) Reflexive : Every element is related to itself in relation

(ii) Symmetric:As per the rule (a, b) R (b, a) R

C- (i)Symmetric- As per the rule (a, b) R (b, a) R

(ii) Irreflexive - No element is related to itself in relation

D- Irreflixe - No element is related to itself in relation

E -Reflexive:- Every element is related to itself in relation

F - None

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