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

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

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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    B
    `A nn B` = singleton set
    C
    `A nn B` = contains two elements
    D
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