<s>[INST] Logical statements: $A+B+C=A+B+C+AB+BC+AC$ 
Let $A,B, C$ be logical statements.
  Then: 
  $A+B+C=A+B+C+AB+BC+AC$

Prove it without a table.

My attempt:
$$A=A\cdot(1+B+C)$$
$$B=B\cdot(1+A+C)$$
$$C=C\cdot(1+A+B)$$
$$\implies A+B+C= A+AB+AC+B+AB+BC+C+BC+AC$$
$$\implies A+B+C=A+B+C+AB+AB+BC+BC+AC+AC$$
$$\implies A+B+C=A+B+C+AB+BC+AC$$
Is this correct?
 [/INST] It's correct, if you are using Monotone laws of Boolean algebra or Logical equivalence, we can write$:$
\begin{align}
&\hspace{3ex}A+B+C\\
&=A+AB+B+BC+C+CA\tag*{Absorption law}\\
&=A+B+C+AB+BC+AC\tag*{Commutative law}
\end{align}
</s>