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Question
If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
reflexive, symmetric and transitive
Solution
Given that, A = {1, 2, 3}.
Let R3 = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}
R3 is reflexive as (1, 1) (2, 2) and (3, 3) ∈ R1
R3 is symmetric as (1, 2), (1, 3), (2, 3) ∈ R1 ⇒ (2, 1), (3, 1), (3, 2) ∈ R1
Therefore, R3 is reflexive, symmetric and transitive.
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