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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
The relation on A having properties of being reflexive, transitive, but not symmetric is
R = {(1, 1), (2, 2), (3, 3), (4, 4), (2, 1)}
Relation R satisfies reflexivity and transitivity.
⇒(1, 1), (2, 2), (3, 3) ∈ R
and (1, 1), (2, 1) ∈ R ⇒(1, 1) ∈ R
However, (2, 1) ∈ R, but (1, 2) ∉ R
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