Let P(S) denote the power set of S = {1, 2, 3, ...., 10}. Define the relations R 1 and R 2 on P(S) as A R 1 B if ( A B C ) ( B A C ) = and A R 2 B if A B C = B A C , A , B P ( S ) . Then [2023]

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Q.
Let P(S) denote the power set of S = {1, 2, 3, ...., 10}. Define the relations $R_{1}$ and $R_{2}$ on P(S) as $A R_{1} B$ if $(A \cap B^{C}) \cup (B \cap A^{C}) = ϕ$ and $A R_{2} B$ if $A \cup B^{C} = B \cup A^{C}, \forall A, B \in P (S)$ . Then [2023]

Solution

Q.
Let P(S) denote the power set of S = {1, 2, 3, ...., 10}. Define the relations $R_{1}$ and $R_{2}$ on P(S) as $A R_{1} B$ if $(A \cap B^{C}) \cup (B \cap A^{C}) = ϕ$ and $A R_{2} B$ if $A \cup B^{C} = B \cup A^{C}, \forall A, B \in P (S)$ . Then [2023]

1 both $R_{1}$ and $R_{2}$ are not equivalence relations

2 only $R_{2}$ is an equivalence relation

3 only $R_{1}$ is an equivalence relation

4 both $R_{1}$ and $R_{2}$ are equivalence relations

Ans.
(4)

(4)

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Solution

Q. Let P(S) denote the power set of S = {1, 2, 3, ...., 10}. Define the relations R1 and R2 on P(S) as AR1B if (A∩BC)∪(B∩AC)=ϕ and AR2B if A∪BC=B∪AC,∀A,B∈P(S). Then [2023]

1 both R1 and R2 are not equivalence relations

2 only R2 is an equivalence relation

3 only R1 is an equivalence relation

4 both R1 and R2 are equivalence relations

Ans. (4)

(4)

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Q.
Let P(S) denote the power set of S = {1, 2, 3, ...., 10}. Define the relations $R_{1}$ and $R_{2}$ on P(S) as $A R_{1} B$ if $(A \cap B^{C}) \cup (B \cap A^{C}) = ϕ$ and $A R_{2} B$ if $A \cup B^{C} = B \cup A^{C}, \forall A, B \in P (S)$ . Then [2023]

1 both $R_{1}$ and $R_{2}$ are not equivalence relations

2 only $R_{2}$ is an equivalence relation

3 only $R_{1}$ is an equivalence relation

4 both $R_{1}$ and $R_{2}$ are equivalence relations

Ans.
(4)