WBJEE · Maths · Sets and Relations
Let \(R\) be the real line. Let the relations \(S\) and \(T\) on \(R\) be defined by \(S=\{(x, y): y=x+1,0 < x < 2\}, T=\{(x, y):(x-y)\) is an integer \(\}\). Then
- A both \(S\) and \(T\) are equivalence relations on \(R\)
- B \(\mathrm{T}\) is an equivalence on \(\mathrm{R}\) but \(\mathrm{S}\) is not
- C neither \(S\) nor \(T\) is an equivalence relation on \(R\)
- D \(\mathrm{S}\) is an equivalence relation on \(\mathrm{R}\) but \(\mathrm{T}\) is not
Answer & Solution
Correct Answer
(B) \(\mathrm{T}\) is an equivalence on \(\mathrm{R}\) but \(\mathrm{S}\) is not
Step-by-step Solution
Detailed explanation
\(\mathrm{T}\) is an equivalence but \(\mathrm{S}\) is not
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