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Question
Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer.
Options
R is reflexive and symmetric but not transitive.
R is reflexive and transitive but not symmetric.
R is symmetric and transitive but not reflexive.
R is an equivalence relation.
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Solution
R is reflexive and transitive but not symmetric.
Explanation:
R is reflexive because (1, 1), (2, 2), (3, 3), (4, 4) ∈ R for all 1, 2, 3, 4 ∈ {1, 2, 3, 4}.
R is not symmetric because (1, 2) ∈ R but (2, 1) ∉ R for all 1, 2, ∈ {1, 2, 3, 4}.
R is transitive because (1, 3) ∈ R and (3, 2) ∈ R.
⇒ (1, 2) ∈ R for all 1, 2, 3 ∈ {1, 2, 3, 4}.
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