Sets of rules to simplify the given logic
Complement
\(A\) complement \(= \overline{A}\) or \(A’\)
\((A’)’ = A\)
AND
\(\begin{aligned} A.A&=A \\ A.0&=0 \\ A.1&=A \\ A.A’&=0 \end{aligned}\)
OR
\(\begin{aligned} A+A&=A \\ A+0&=A \\ A+1&=1 \\ A+A’&=1 \end{aligned}\)
Distributive Law
\(\begin{aligned} A.(B+C) &= A.B+A.C \\ A+(B.C) &= (A+B).(A+C) \end{aligned}\)
from there, we can get
\(\begin{aligned} A’+AB &= A’+B \\ A+A’B &= A+B \end{aligned}\)
Commutative Law
\(\begin{aligned}A.B &= B.A \\ A+B&= B+A\end{aligned}\)
Associative Law
\(\begin{aligned} (A.B).C &= A.(B.C) \\ (A+B)+C &= A+(B+C) \end{aligned}\)
De Morgans Law
\(\begin{aligned} \overline{(A+B)}&=\overline{A}.\overline{B} \\ \overline{A.B}&=\overline{A}+\overline{B} \end{aligned}\)
Absorption Law
\(\begin{aligned} A+A.B &= A \\ A.(A+B) &= A \end{aligned}\)