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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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The correct answer is:
inverse law is not satisfied
Under the binary operation,
$\mathrm{A} * \mathrm{~B}=\mathrm{A} \cup \mathrm{B}, \forall \mathrm{A}, \mathrm{B} \in \mathrm{P}(\mathrm{x})=$ Power set
Inverse of 'A' does not exists because
$$
A * B \neq \phi \text {, for any } B \in P(x)
$$
Where $\phi$ is the identity element in $P(x)$.
While under the binary operation $A * B=A \cup B$, the commutative law, associative law and identity elements are exists.
$\mathrm{A} * \mathrm{~B}=\mathrm{A} \cup \mathrm{B}, \forall \mathrm{A}, \mathrm{B} \in \mathrm{P}(\mathrm{x})=$ Power set
Inverse of 'A' does not exists because
$$
A * B \neq \phi \text {, for any } B \in P(x)
$$
Where $\phi$ is the identity element in $P(x)$.
While under the binary operation $A * B=A \cup B$, the commutative law, associative law and identity elements are exists.
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