How to prove that $b \wedge 0 = 0$ in a boolean algebra?

Question

It seems a rather obvious fact, but how can we prove that $b \wedge 0 = 0$ for an arbitrary element $b$ in a boolean algebra. Where $0 := c \wedge - c$ for any element $c$ of the boolean algebra, and the axioms for complement are $(b \wedge -b) \vee c = c$, and $(b \vee - b) \wedge c = c$.

Answer 1

Hint: Since $0=c\wedge -c$ for any $c$, you can pick some specific $c$. Try taking $c=b$.