Question:
Let R = {(a, a), (b, b), (c, c), (a, b)} be a relation on set A = a, b, c. Then, R is
(a) identify relation
(b) reflexive
(c) symmetric
(d) antisymmetric
Solution:
(b) reflexive
Reflexivity : Since $(a, a) \in R \forall a \in A, R$ is reflexive on $A$.
Symmetry: Since $(a, b) \in R$ but $(b, a) \notin R, R$ is not symmetric on $A$.
$\Rightarrow R$ is not antisymmetric on $A$.
Also, $R$ is not an identity relation on $A$.
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