Consider the following relations on {1, 2, 3, 4}. Which of the following relations 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)}
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Correct answer: D. (C) and (E) Only
Explanation
A reflexive relation must contain (1,1), (2,2), (3,3) and (4,4). R₁ misses (3,3), R₂ misses (3,3) and (4,4), and R₄ has no loops. Only R₃ and R₅ contain all four pairs.More Discrete Structures and Optimization questions
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