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Question:

If A = {abcd}, then a relation R = {(ab), (ba), (aa)} on A is

(a) symmetric and transitive only
(b) reflexive and transitive only
(c) symmetric only
(d) transitive only

Solution:

(a) symmetric and transitive only

Reflexivity: Since $(b, b) \notin R, R$ is not reflexive on $A$.

Symmetry : Since $(a, b) \in R$ and $(b, a) \in R, R$ is symmetric on $A$.

Transitivity : Since $(a, b) \in R, \quad(b, a) \in R$ and $(a, a) \in R, R$ is transitive on $A$.

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