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If $\mathrm{A}=\{1,2,3,4\}$ and $\mathrm{R}=\{(1,1),(1,3),(2,2),(3,1),$,
$(3,4),(4,3),(4,4)\}$ is a relation on $A \times A$, then which one of the following is correct?
Options:
$(3,4),(4,3),(4,4)\}$ is a relation on $A \times A$, then which one of the following is correct?
Solution:
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Verified Answer
The correct answer is:
$R$ is neither reflexive nor transitive
Since, $3 \in \mathbf{A}$
but $(3,3) \notin \mathrm{R}$
So, it is notreflexive. and $(3,4) \in \mathrm{R}$ and $(4,3) \in \mathrm{R}$
but $(3,3) \notin \mathrm{R}$
So, it is also not transitive. Hence, $R$ is neither reflexive nor transitive.
but $(3,3) \notin \mathrm{R}$
So, it is notreflexive. and $(3,4) \in \mathrm{R}$ and $(4,3) \in \mathrm{R}$
but $(3,3) \notin \mathrm{R}$
So, it is also not transitive. Hence, $R$ is neither reflexive nor transitive.
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