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Question
Let R be the relation on the set A = {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Then, _____________________ .
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.
Reflexivity: Clearly, (a, a) ∈ R ∀ a ∈A
So, R is reflexive on A.
Symmetry : Since (1, 2) ∈ R, but (2, 1) ∉ R,
R is not symmetric on A.
Transitivity : Since, (1, 3), (3, 2) ∈ R and (1, 2) ∈ R,
R is transitive on A.
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