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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?
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Solution
We have,
R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}
As, (a,a) ∈ R∀a ∈ A
So, R is a reflexive relation
Also, (a,b) ∈ R and (b,a)∈ R
So, R is a symmetric relation as well
And, (0,1) ∈ R but (1,2) ∉ R and (2,3) ∉ R
So, R is not a transitive relation
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