KCET · Maths · Mathematical Reasoning
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
- A identity law is not satisfied
- B inverse law is not satisfied
- C commutative law is not satisfied
- D associative law is not satisfied
Answer & Solution
Correct Answer
(B) inverse law is not satisfied
Step-by-step Solution
Detailed explanation
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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