$(a\neq -1\ \wedge\ b\neq -1)\implies (a+b+ab\neq -1)$ Using proof by contrapositive

Question

Let A,B be two real numbers, using proof by contrapositive, show the following implication: $(a\neq -1\ \ and \ \ b\neq -1)\implies (a+b+ab\neq -1)$

I applied it's contrapositive

$(a+b+ab=-1)\implies (a=-1\ or\ b = -1$)

But I'm currently stuck in proving the implication because it has OR.

Answer 1

1+a+b+ab=(1+a)(1+b)=0 implies a=-1 or b=-1

Answer 2

I think you're meant to assume the antecedent in your question, deduce the consequent AND THEN apply the contrapositive.

Answer 3

Hint: $a + b + ab = -1$ iff $a(1+b) = -(1+b)$. If $b \neq -1$, then you can divide this through by $1 + b$. (I.e., one strategy to prove the disjunction $a = -1$ or $b = -1$ is to assume on of the disjuncts is false and use that fact to prove the other disjunct.)