WBJEE · Maths · Sets and Relations
If \(R\) and \(\mathrm{R}^1\) are equivalence relations on a set \(A\), then so are the relation
- A \(\mathrm{R}^{-1}\)
- B \(\mathrm{R} \cup \mathrm{R}^1\)
- C \(\mathrm{R} \cap \mathrm{R}^1\)
- D All of these
Answer & Solution
Correct Answer
(C) \(\mathrm{R} \cap \mathrm{R}^1\)
Step-by-step Solution
Detailed explanation
Hint: If \(R ~\&~ R^1\) are equivalence relation \(\mathrm{R}^{-1} \Rightarrow\) Equivalence \(\mathrm{R} \cap \mathrm{R}^1 \Rightarrow\) Equivalence \(R \cup R^1\) may or may not equivalence
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