Let A = {0, 1, 2, 3} and R be a relation on A defined as
Question:

Let A = {0, 1, 2, 3} and R be a relation on A defined as
R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}
Is R reflexive? symmetric? transitive?

Solution:

We have,

$R=\{(0,0),(0,1),(0,3),(1,0),(1,1),(2,2),(3,0),(3,3)\}$

As, $(a, a) \in R \forall a \in A$

So, $R$ is a reflexive relation

Also, $(a, b) \in R$ and $(b, a) \in R$

So, $R$ is a symmetric relation as well

And, $(0,1) \in R$ but $(1,2) \notin R$ and $(2,3) \notin R$

So, $R$ is not a transitive relation

 

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