Let \( R \) be the real line. Consider the following subsets of the...

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Let \( R \) be the real line. Consider the following subsets of the plane \( R \times R \)
\( \mathrm{P} \)
\( \mathrm{S}=\{(x, y): y=x+1 \) and \( 0x2\} \)
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\( \mathrm{T}=\{(x, y): x-y \) is an integer \( \} \)
Which of the following is true?
(1) Both \( \mathrm{S} \) and \( \mathrm{T} \) are equivalence relations on \( R \)
(2) \( \mathrm{S} \) is equivalence relation but \( \mathrm{T} \) is not
(3) \( \mathrm{T} \) is an equivalence relation but \( \mathrm{S} \) is not
(4) Neither \( \mathrm{S} \) nor \( \mathrm{T} \) are equivalence relations
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