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Question
If A = {a, b, c, d}, then a relation R = {(a, b), (b, a), (a, a)} on A is _____________ .
Options
symmetric and transitive only
reflexive and transitive only
symmetric only
transitive only
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Solution
symmetric and transitive only
Reflexivity: Since (b, b) ∉ R, R is not reflexive on A.
Symmetry: Since (a, b) ∈ R and (b, a) ∈ R, R is symmetric on A.
Transitivity: Since (a, b) ∈ R, (b, a) ∈ R and (a, a) ∈ R, R is transitive on A
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