First slide

Relations XII

Question

Let $R = \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\}$ be a relation on the set $A = \{1, 2, 3, 4\} .$ The relation R is

Easy

A

Reflexive
B

Transitive
C

Not symmetric
D

A function

Solution

Given $A = \{1, 2, 3, 4\}$
$R = \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\}$
$(2, 3) \in R but (3, 2) \notin R$ . Hence R is not symmetric.
R is not reflexive as $(1, 1) \notin R .$
R is not a function as $(2, 4) \in R and (2, 3) \in R .$
R is not transitive as $(1, 3) \in R and (3, 1) \in R$ but $(1, 1)$ $\notin R .$

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