In P(X) , the power set of a non-empty set X , an binary operation * is defined by A^* ~B=A ∪ B, ∀ A, B ∈ P(x) under * , a true statement is

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MARKS Content Team · Accepted Answer

Correct answer: (B) inverse law is not satisfied. Under the binary operation, A * ~B=A ∪ B, ∀ A, B ∈ P(x)= Power set Inverse of 'A' does not exists because A * B ≠ φ , for any B ∈ P(x) Where φ is the identity element in P(x) . While under the binary operation A * B=A ∪ B , the commutative law, associative law and identity elements are exists.

In $P(X)$, the power set of a non-empty set $X$, an binary operation * is defined by $\mathrm{A}{ }^{} \mathrm{~B}=\mathrm{A} \cup \mathrm{B}, \forall \mathrm{A}, \mathrm{B} \in \mathrm{P}(\mathrm{x})$ under $$, a true statement is

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Relevant Questions

In $P(X)$, the power set of a non-empty set $X$, an binary operation * is defined by $\mathrm{A}{ }^{*} \mathrm{~B}=\mathrm{A} \cup \mathrm{B}, \forall \mathrm{A}, \mathrm{B} \in \mathrm{P}(\mathrm{x})$ under $*$, a true statement is

Solution

Relevant Questions

In $P(X)$, the power set of a non-empty set $X$, an binary operation * is defined by $\mathrm{A}{ }^{} \mathrm{~B}=\mathrm{A} \cup \mathrm{B}, \forall \mathrm{A}, \mathrm{B} \in \mathrm{P}(\mathrm{x})$ under $$, a true statement is