Logic and Boolean Algebra

In Boolean notation $AB = 1$ only when $A = 1$ and $B = 1$.

$2^n$ rows for $n$ inputs, so $2^3 = 8$.

Factorising gives $A(B + B') = A \cdot 1 = A$. Whatever $B$ does, the output follows $A$.

Break the bar and change the sign: 'not (A or B)' means 'neither A nor B'.

Expanding gives $AA + AB = A + AB = A(1+B) = A$. This is the other absorption law.

The value of $A$ becomes irrelevant. Note this is not ordinary addition — there is no value 2 in Boolean algebra.