Consider the following relations on {1, 2, 3, 4}. Which of them are reflexive? (A) R₁ = {(1,1), (1,2), (2,1), (2,2), (3,4), (4,1), (4,4)} (B) R₂ = {(1,1), (1,2), (2,1)} (C) R₃ = {(1,1), (1,2), (1,4), (2,1), (2,2), (3,3), (4,1), (4,4)} (D) R₄ = {(2,1), (3,1), (3,2), (4,1), (4,2), (4,3)} (E) R₅ = {(1,1), (1,2), (1,3), (1,4), (2,2), (2,3), (2,4), (3,3), (3,4), (4,4)}

1. A(A), (B) and (C) Only
2. B(A), (D) and (E) Only
3. C(D) and (E) Only
4. D(C) and (E) Only

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Correct answer: D. (C) and (E) Only

Explanation

A relation on {1,2,3,4} is reflexive only if it contains (1,1), (2,2), (3,3) and (4,4). Only R₃ and R₅ contain all four.