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

Answer 1

$\underline{\textsf{Given:}}$

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

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

$\underline{\textsf{To find:}}$

$\textsf{The value of p-q}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

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

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

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

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

$\textsf{Equating powers on bothsides we get}$

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