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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2010

  • question_answer
    In P(X), the power set of a non-empty set X, an binary operation * is defined by\[A\,*\,B=A\cup B,\forall A,B\in P(x)\] 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

    Correct Answer: B

    Solution :

    Under the binary operation, \[A*B=A\cup B,\forall A,B\in P(x)=\]power set Inverse of ‘A’ does not exists because                 \[A*B\ne \phi ,\] 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 identify elements are exists.


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