Reasoning and Logic

A proposition is any statement with a definite truth value. Being false does not stop it being a proposition.

$2^n$ rows for $n$ propositions, so $2^4 = 16$.

By De Morgan, $\neg(p \wedge q) \equiv \neg p \vee \neg q$. Each part is negated and 'and' becomes 'or'.

The contrapositive is $\neg q \to \neg p$: swap the two parts and negate both. It is logically equivalent to the original.

One counterexample destroys a universal claim. Any value strictly between 0 and 1 works, as does $x = 1$, where the two are equal.

If $p$ is true, $p \vee q$ is true, so the conjunction is true. If $p$ is false, the conjunction is false whatever $q$ does. So the value always matches $p$. This is the absorption law.