What $P(E)\sim (E \to \{ 0,1\} )$ mean?

Question

i was asked to prove: $P(E)\sim (E \to \{ 0,1\} )$.

the left-hand side is the set of all subsets of $E$. (Right?)
What about the right-hand side?

Thanks.

Answer 1

Most probably it denotes the set of all functions $E\to \{0,1\}$.

Note that this is usually rather denoted by exponentiation: $\{0,1\}^E$.

Answer 2

The set of all functions from $E$ to $\{0,1\}$.