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.

Answers (1)

A = \{}1, 2, 3, 4\}

R = \{(1, 2), (2, 2), (1, 1), (4,4), (1, 3), (3, 3), (3, 2)\}

For every  a \in A  there is  (a,a) \in R

\therefore R is reflexive.

Given, (1,2) \in R  but  (2,1) \notin R 

\therefore R is not symmetric.

For  a,b,c \in A there are (a,b) \in R \, and \, (b,c) \in R  \Rightarrow (a,c) \in R

\therefore R is transitive.

Hence, R  is reflexive and transitive but not symmetric.

The correct answer is option B.

 

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