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Let R be the real line. Consider the ...

Let R be the real line. Consider the following subsets of the plane `RxxR` . `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? (1) neither S nor T is an equivalence relation on R (2) both S and T are equivalence relations on R (3) S is an equivalence relation on R but T is not (4) T is an equivalence relation on R but S is not

A

T is an equivalence relation on R but S is not

B

Neither S nor T is an equivalence relation on R

C

Both S and T are equivalence relations on R

D

S is an equivalence relation on R but T is not

Text Solution

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The correct Answer is:
A
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