Let PRIMESAT = {F ∈ SAT: the number of truth assignments t that satisfies F is a prime number}. Prove that SAT∈ 𝐵𝑃 (PRIMESAT). Prove that the class ⊕𝑃 is closed under the Boolean operations union,...

Let PRIMESAT = {F ∈ SAT: the number of truth assignments t that satisfies F is a prime number}. Prove that SAT∈ 𝐵𝑃 (PRIMESAT).

Prove that the class ⊕𝑃 is closed under the Boolean operations union, intersection, and complementation.