Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer.
A) R is reflexive and symmetric but not transitive.
(B) R is reflexive and transitive but not symmetric.
(C) R is symmetric and transitive but not reflexive.
(D) R is an equivalence relation.
$R=\{(1,2),(2,2),(1,1),(4,4),(1,3),(3,3),(3,2)\}$
It is seen that $(a, a) \in \mathbf{R}$, for every $a \in\{1,2,3,4\}$.
∴ R is reflexive.
It is seen that $(1.2) \in R$. but $(2.1) \notin R$.
∴R is not symmetric.
Also, it is observed that $(a, b),(b, c) \in \mathrm{R} \Rightarrow(a, c) \in \mathrm{R}$ for all $a, b, c \in\{1,2,3,4\}$.
∴ R is transitive.
Hence, R is reflexive and transitive but not symmetric.
The correct answer is B.
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