I've been trying to interpret a logical proposition for several days. I need to simplify, I can't do it with the laws that I know, but using online tools I can find the result, but in the step by step a method appears that I don't know
The question is: In the next table what does it mean: "introduce Variables" (I know the other laws)
where does (A+A’) come from
the proposition is: [(A’B’) + (A’+C)’]’ (B’C’)’
The Solution is:
| [(A’B’)+(A’+C)’]’ (B’C’)’ | Defininition |
|---|---|
| (A+B)(A’+C’’)(B’C’)’ | De morgan Law |
| (AA’ + AC + BA’ + BC) (B’C’)’ | Distrib Law |
| (0 + AC + BA’ + BC) (B’C’)’ | Complement Law |
| (AC + BA’ + BC) (B’C’)’ | Identity Law |
| (AC + BA’ + BC) (B’’+C’’) | De morgan Law |
| ACB + ACC +BA’B + BA’C + BCB + BCC | Distrib Law |
| ACB + CA + BA’B + BA’C + BCB + BCC | Idemp Law |
| AC + BA’B + BA’C + BCB + BCC | Absorpt Law |
| AC + BA’ + BA’C + BCB + BCC | Idemp Law |
| BA’ + AC + BCB + BCC | Absorpt Law |
| BC + BA’ + AC | Idemp Law |
| BC (A+A’) + BA’ + AC | Introduce Variables |
| BCA + BCA’ + BA’ + AC | Distrib Law |
| AC + BA’ | Absorpt Law |
| AC + BA’ | Answer |
Note: Other sites call this step: Consensus
Thanks a lot, my head is going to explode, I can't find anything on the internet to guide me.