Let $A = (Q,Σ,\delta,q_0,F)$ be an NFA such that $L = L(A)$.
We define a DFA $A'=(Q',Σ,\delta,q_0',F')$ as: $$ Q'=2^Q, \qquad q_0'=\{q_0\}\\F'=\{q\in Q \mid q'\cap F \neq\emptyset\} $$ My question is how we know what elements $Q'$ has? What is the formal definition to obtain these elements? Because it can contain all elements of $2^Q$, and in the DFA obtained from a NFA, the states are not all the elements of $2^Q$.