# Let

Question:

Let R = {(aa), (bb), (cc), (ab)} be a relation on set A = abc. 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 $A$.