Let R be the real line. Consider the following subsets of the plane R R. S = (x, y) : y = x + 1 and 0 < x < 2 , T = (x, y) : x - y is an integer . Which one of the following is true?

JEE Main 2008 Mathematics question

Let R be the real line. Consider the following subsets of the plane . and , is an integer . Which one of the following is true?

Answer: (4)

S is not reflexive ((1, 1) ∉ S since y ≠ x), so it is not an equivalence relation. T: x − x = 0 is an integer (reflexive); if x − y

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Question ID VK-039091