Mark the tick against the correct answer in the following:
Let $A=\{1,2,3\}$ and let $R=\{(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)\} .$ Then, $R$ is
A. reflexive and symmetric but not transitive
B. symmetric and transitive but not reflexive
C. reflexive and transitive but not symmetric
D. an equivalence relation
Given set $A=\{1,2,3\}$
And $R=\{(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)\}$
Formula
For a relation $R$ in set $A$
Reflexive
The relation is reflexive if $(a, a) \in R$ for every $a \in A$
Symmetric
The relation is Symmetric if $(a, b) \in R$, then $(b, a) \in R$
Transitive
Relation is Transitive if $(a, b) \in R \&(b, c) \in R$, then $(a, c) \in R$
Equivalence
If the relation is reflexive, symmetric and transitive, it is an equivalence relation.
Check for reflexive
Since, $(1,1) \in R,(2,2) \in R,(3,3) \in R$
Therefore, $R$ is reflexive $\ldots \ldots$ (1)
Check for symmetric
Since, $(1,2) \in R$ and $(2,1) \in R$
$(2,3) \in R$ and $(3,2) \in R$
Therefore, $R$ is symmetric ....... (2)
Check for transitive
Here,$(1,2) \in R$ and $(2,3) \in R$ but $(1,3) \notin R$
Therefore, $\mathrm{R}$ is not transitive ....... (3)
Now, according to the equations (1), (2), (3)
Correct option will be (A)
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.