Let P(S) denote the power set of S = {1, 2, 3, …, 10}. Define the relations R₁ and R₂ on P(S) as A R₁ B if (A…

Question

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

Accepted Answer

A. Both $$R_1$$ and $$R_2$$ are equivalence relations.

Answer

B. Only $$R_1$$ is an equivalence relation.

Answer

C. Only $$R_2$$ is an equivalence relation.

Answer

D. Both $$R_1$$ and $$R_2$$ are not equivalence relations.

Answer & step-by-step solution

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