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For any sets A and B. show that P(A nnB...

For any sets A and B. show that `P(A nnB) = P(A)nn P(B)dot`

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let `P(A nn B) , P(A), P(B) `are the power sets of the set `A nn B , A, B` respectively
let c is a set where `C in P(A nnB)`
elements of C`in (A nn B)`
so, `C in A`
`C in B`
so, `C in P(A) & C in P(B)`
`C in [ P(A) nn P(B)]` = LHS
hence proved
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Knowledge Check

  • For any two events A and B, if P (A uu B) = P ( A nn B, then

    A
    `P (A) = P (B)`
    B
    `P (A) gt P (B)`
    C
    `P (A) lt P (B)`
    D
    None of these

  • For any two events A and B if P (A uu B) = 5//6, P (A nn B) = 1//3, P (B) = 1//2 then P (A) is

    A
    `1//2`
    B
    `2//3`
    C
    `1//3`
    D
    None of these

  • A and B are any two sets such that n(A)gtn(B) . P(A) and P(B) are power sets of A and B, respectively, and the difference between cardinal numbers of P(A) and P(B) is a three - digit prime number. The number of elements in set A is ___________.

    A
    6
    B
    7
    C
    5
    D
    None of these
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