Q111 / 155 · WBJEE 2023 · Mathematics

If \(R\) and \(\mathrm{R}^1\) are equivalence relations on a set \(A\), then so are the relation

Correct answer
A
\(\mathrm{R}^{-1}\)
B
\(\mathrm{R} \cup \mathrm{R}^1\)
Correct answer
C
\(\mathrm{R} \cap \mathrm{R}^1\)
D
All of these

Solution

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

Hence, the correct answer is options: 'A', 'C'.

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