Question regarding wffs sets, and satisfiability.

Question

Let A and B be satisfiable (in the way the term is used in mathematical logic, with wffs, etc.).

How do I show that the union and intersection of A and B are both also satisfiable? I'm slightly lost, and would appreciate any help.

Cheers!

Answer 1

Suppose $M\models A$ and $N\models B$, since $A\cap B\subseteq A$ and $B$, so $M\models A\cap B$ and $N\models A\cap B$ . For the union, as Andre Nicolas mentioned, it need not be satisfiable, just think $A$ and $B$ both have a single sentence which is the negation of each other.