1.

Let R be the set of all real numbers. Consider the following subsets of the plane R x R: S = {(x, y): y = x + 1 and 0 < x < 2} and T = {(x, y) : x – y is an integer} Then which of the following is true? (a) T is an equivalence relation but S is not an equivalence relation. (b) Neither S nor T is an equivalence relation (c) Both S and T are equivalence relation (d) S is an equivalence relation but T is not an equivalence relation.

Answer»

(a) T is an equivalence relation but S is not an equivalence relation.

(0, 1), (1, 2) it is not an equivalence relation T is an equivalence relation



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