If R and (R^1) are equivalence relations on a set A , then so are...

R

and (\mathrm{R}^1) are equivalence relations on a set

A

, then so are the relation

Options

A(\mathrm{R}^{-1})
B(\mathrm{R} \cup \mathrm{R}^1)
C(\mathrm{R} \cap \mathrm{R}^1)
DAll of these

Correct answer

C. (\mathrm{R} \cap \mathrm{R}^1)

Step-by-step solution

Hint: If (R ~\&~ R¹) are equivalence relation (\mathrm{R}^{-1} \Rightarrow) Equivalence (\mathrm{R} \cap \mathrm{R}^1 \Rightarrow) Equivalence (R \cup R¹) may or may not equivalence

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