How to tell if this propositional logic statement is valid?

Question

$$W ∧ X ∧ Y ⊨ Z \text{ if and only if } ⊨ W → (X → (Y → Z))$$

I know it can be done using truth tables but I'm stuck on the "if and only if ⊨", I don't understand what that means.

Answer 1

'A if and only if B' is written symbolically as $ A \iff B$ and it means that whenever A happens B happens too and whenever $B$ happens $A$ happens too. It is just math talk for: "these things imply one another." Your truth table calculations should reveal that these two things always imply one another.