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Question
If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
reflexive, transitive but not symmetric
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Solution
Given that, A = {1, 2, 3}.
Let R1 = {(1, 1), (1, 2), (1, 3), (2, 3), (2, 2), (1, 3), (3, 3)}
R1 is reflexive as (1, 1), (2, 2) and (3, 3) lie is R1.
R1 is transitive as (1, 2) ∈ R1, (2, 3) ∈ R1 ⇒ (1, 3) ∈ R1
Now, (1, 2) ∈ R1 ⇒ (2, 1) ∉ R1.
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