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Question
Given an example of a relation. Which is symmetric and transitive but not reflexive.
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Solution
Let A = {1, 2}.
Define a relation R on A as:
R = {(1, 1)}
R is symmetric, because if (1, 1) ∈ R, then (1, 1) ∈ R.
R is transitive, because (1, 1) and (1, 1) imply (1, 1) ∈ R.
R is not reflexive, because (2, 2) ∉ R.
Hence, R is symmetric and transitive but not reflexive.
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