Let $P(\mathrm{S})$ denote the power set of $S=\{1,2,3, . . ., 10\}$. Define the relations $R_1$ and $R_2$ on $P(\mathrm{S})$ as $AR_1B$ if $(A \cap B^c) \cup (B \cap A^c)=\phi$ and $AR_2\ B$ if $A \cup B^c=B \cup A^c, \forall A, B \in P(S)$ . Then :

Question

Dr. Abubacker · Accepted Answer

The correct answer is Option A: both $R_1$ and $R_2$ are equivalence relations.

Q. Let $P(\mathrm{S})$ denote the power set of $S=\{1,2,3, . . ., 10\}$. Define the relations $R_1$ and $R_2$ on $P(\mathrm{S})$ as $AR_1B$ if $(A \cap B^c) \cup (B \cap A^c)=\phi$ and $AR_2\ B$ if $A \cup B^c=B \cup A^c, \forall A, B \in P(S)$ . Then :

Explanation

Reviewed by Dr. Abubacker

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