Which of the following is correct, if P(A) is power set of the set A?

Which of the following is correct, if P(A) is power set of the set A?

  1. A

    P(A)P(B)=P(AB)

  2. B

    P(A)P(B)=P(AB)

  3. C

    P(A)P(B)=P(AB)

  4. D

    None of these 

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    Solution:

    ABA and ABB

       P(AB)P(A) and P(AB)P(B) 

    P(AB)P(A)P(B)                                            ..(i)

    Now, CP(A)P(B)

    CP(A) and CP(B)CA and CBCABCP(AB)

    P(A)P(B)P(AB)                                            …(ii)

    From (i) ,from  (ii), 

    P(AB)=P(A)P(B)

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