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If $A=\{a, b, c\}$ and $R=\{(a, a),(a, b),(b, c),(b, b),(c, c),(c, a)\}$
is a binary relation of $A$, then which one of the following is
correct?
Options:
is a binary relation of $A$, then which one of the following is
correct?
Solution:
1913 Upvotes
Verified Answer
The correct answer is:
$R$ is reflexive, but neither symmetric nor transitive
Let $\mathrm{A}=\{a, b, c\}$ and
$\mathrm{R}=\{(a, a),(a, b),(b, c),(b, b),(c, c),(c, a)\}$
Since, $(a, a),(b, b),(c, c) \in k$
$R$ is reflexive relation But $(a, b) \in R$ and $(b, a) \notin R$ $R$ is not symmetric relation. Also, $(a, b),(b, c) \in \bar{k}$
$\Rightarrow(c, a) \in R$ But $(a, c) \in R$
$R$ isnot transitive relations.
$\mathrm{R}=\{(a, a),(a, b),(b, c),(b, b),(c, c),(c, a)\}$
Since, $(a, a),(b, b),(c, c) \in k$
$R$ is reflexive relation But $(a, b) \in R$ and $(b, a) \notin R$ $R$ is not symmetric relation. Also, $(a, b),(b, c) \in \bar{k}$
$\Rightarrow(c, a) \in R$ But $(a, c) \in R$
$R$ isnot transitive relations.
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