Writing a Proof by Contrapositive: ab = 0 and De Morgan

Write the full proof, opening with a sentence announcing the contrapositive and citing the earlier result that a product of odd integers is odd, with $x = y = n$.

Write $\neg(a \ne 0 \wedge b \ne 0) \equiv (a = 0) \vee (b = 0)$ and use it to state the contrapositive of: if $a \ne 0$ and $b \ne 0$, then $ab \ne 0$.

Record $X \to (Y \vee Z) \equiv (X \wedge \neg Y) \to Z$, restate the contrapositive as: if $ab = 0$ and $a \ne 0$, then $b = 0$, and prove it using $\frac{1}{a}$.