Let R be the real line. Consider the following subsets of the plane R×R.S={(x,y):y=x+1and0<x<2},T={(x,y):x−yis an integer }. Which one of the following is true?

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Let R be the real line. Consider the following subsets of the

Question

Let R be the real line. Consider the following subsets of the plane $R \times R$ . $S = {(x, y) : y = x + 1 a n d 0 < x < 2}, T = {(x, y) : x - y$ is an integer }. Which one of the following is true?

neither S nor T is an equivalence relation on R

both S and T are equivalence relations on R

S is an equivalence relation on R but T is not

T is an equivalence relation on R but S is not

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Lucas Discussed

Let R be the real line. Consider the following subsets of the plane

R \times R

S = {(x, y) : y = x + 1 a n d 0 < x < 2}, T = {(x, y) : x - y

is an integer }. Which one of the following is true?

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Question Text

Let R be the real line. Consider the following subsets of the plane

R \times R

S = {(x, y) : y = x + 1 a n d 0 < x < 2}, T = {(x, y) : x - y

is an integer }. Which one of the following is true?