A relation R on A = {1, 2, …, 12} is R = {(x, y) : 2x − y = 0}. Which statement is true?
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Answer: C. R is neither reflexive, nor symmetric, nor transitive
R = {(1,2), (2,4), (3,6), (4,8), (5,10), (6,12)}. (1,1) ∉ R, so not reflexive; (1,2) ∈ R but (2,1) ∉ R, so not symmetric; (1,2), (2,4) ∈ R but (1,4) ∉ R, so not transitive.