If n(a) = p and n(b) = q and total number of subsets of a is 16 times, that of b then p – q

Question

If n(a) = p and n(b) = q and total number of subsets of a is 16 times, that of b then p – q

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Vivian 2 months 2021-11-23T07:24:19+00:00 1 Answer 0 views 0

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    2021-11-23T07:26:09+00:00

    \underline{\textsf{Given:}}

    \textsf{n(A)=p and n(B)=q}

    \mathsf{n[P(A)]=16\,n[P(B)]}

    \underline{\textsf{To find:}}

    \textsf{The value of p-q}

    \underline{\textsf{Solution:}}

    \textsf{Consider,}

    \mathsf{n[P(A)]=16\,n[P(B)]}

    \mathsf{2^p=16(2^q)}

    \mathsf{\dfrac{2^p}{2^q}=16}

    \mathsf{2^{p-q}=2^4}

    \textsf{Equating powers on bothsides we get}

    \boxed{\mathsf{p-q=4}}

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