Modulo of a power set

Question

So I am given a modulo of a set A, say 5. I know that the formula for the modulo of the power set is 2^5 however I am not sure why that is the actual formula. (2^n where n is the modulo of the set)

Would anyone be able to explain?

Here's the actual question as I think I'm not fully understanding the question correctly. enter image description here

Thanks in advance :)

Answer 1

You mean the cardinality of the power set.

For each element in $A$, there are two options, we have to decide whether to include it in a subset or exclude it, hence the formula of $2^n$ by multiplicative principle.