I'm trying to solve the highlighted part. I understand how they got the left side of the equation. They wrote out the truth table for a or b and then negated it. Easy. However for the right side I am totally confused.
I thought for for the inclusive disjunction, you need atleast 1 true from either propisition for the disjunction to be true.
In short, What I'm asking is how you think when you're solving the right side.
$\wedge$ is the logical conjunction. $A\wedge B$ is true if and only if both $A$ and $B$ are true. Hence the proposition $(\neg A)\wedge(\neg B)$ is true if and only if the propositions $\neg A$ and $\neg B$ are both true, which only happens in the last row of the truth table you show.