Values of a and b in a power set

Question

The question that I am trying to answer is the following:

*Two sets A and B contains a and b elements respectively. If power set of A contains 8 more elements than that of B, value of ‘b’ and ‘a’ are respectively

a) 3, 4

b) 5, 6

c) 1, 2

d) None of the mentioned*

I assumed that by 'value', the size or cardinality is meant. And so, I just simply used 2^n.

By plugging in 3 and 4, I got 8 and 16 respectively. Since the question mentions that A has eight more elements, then I supposed that my answer, letter A, satisfies that because the difference of 16 and 8 is 8.

Is my assumption correct, or did I do something along the way?

Answer 1

You did it right.

A set with $n$ elements has a power set of cardinality $2^n$.