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1.Relation and Function
medium
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
A
Reflexive
B
Transitive
C
Not symmetric
D
A function
(AIEEE-2004)
Solution
(c) 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 $(1, 3) \in R\ and\,\,\, (3, 1) \in R\ but (1, 1) \notin R.$
Standard 12
Mathematics
