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Question
Give an example of a relation which is reflexive and transitive but not symmetric?
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Solution
Let a relation R be defined on a set R.
R = {(a, b) : a3 ≥ b3}
Therefore, (a, a) ∈ R ......[because a3 = a3]
∴ R is Reflexive. ..... [because 23 ≥ 13]
Here, (2, 1) ∈ R .....[because 13 ≥ 23]
∴ R is not symmetric.
Now, let (a, b) and (b, c) ∈ R.
∴ R is transitive.
Hence, the relation R is reflexive and transitive but not symmetric.
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