If P is satisfiable and Q is satisfiable, is P^Q satisfiable?

Question

This question is confusing me,

Is the following statement true?

If P is satisfiable and Q is satisfiable then P∧Q is satisfiable.

I originally thought this was true because when drawing a truth table I find that if P and Q are true, then P∧Q is true too, but my answer sheet says that the statement is false. Why is that?

Answer 1

Consider $Q = \neg P$, but $P$, $Q$ both satisfiable.