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Let a set A = A = A1 ∪ A2 ∪...∪ Aki where Ai ∩ Aj = ϕ for i ≠ j 1 ≤ k. Define the relation R from A to A by R = {(x,y) : y ∈ Ai if and only if x ∈ Ai , 1 ≤ i ≤ K}. Then is(A) reflexive, symmetric but not transitive (B) reflexive, transitive but not symmetric (C) reflexive but not symmetric and transitive (D) an equivalence relation |
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Answer» (D) an equivalence relation A = {1, 2, 3} R = {(1, 1), (1, 2), (1, 3) (2, 1), (2, 2), (2, 3) (3,1), (3, 2) (3, 3)} |
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