Question

Sejam A e B dois conjuntos tais que n(A)=n(B)+6. Então, o valor de n(P(A))/n(P(B)) é igual a

a) 8

b) 16

c) 32

d) 64

e) 128

Answer 1

n(P(A)) = 2ⁿ
n(A) = n(B) + 6  , n(B) = n(A) - 6

$n(P(A))=2^{n(B)+6} = 2 ^{6} . 2^{n(B)} =64. 2^{n(B)} \\ \\ n(P(B))= 2^{n(A)-6} = \frac{ 2^{n(A)} }{2 ^{6} } = \frac{ 2^{n(A)} }{64} \\ \\ \frac{n(P(A))}{n(P(B))} =64. 2^{n(B)} : \frac{ 2^{n(A)} }{64} = \frac{64. 2^{n(B)}.64 }{ 2^{n(A)} } = \frac{64. 2^{n(B)}.64 }{ 2^{n(B)+6} } = \\ \\ \frac{64 .2^{n(B)}.64 }{ 2^{6} 2^{n(B)} } = \frac{64.64. 2^{n(B)} }{64. 2^{n(B)} } =64$

Letra D