# What is the simplification of AB + BC + (~B)C?

AB + C is not the answer. The correct answer is AB + BC. HOW?

• How should ~BC be parsed? ​ ​ – user12859 Feb 26 '17 at 3:57
• ~ sign is for negation, it's (not)B. Did you mean to ask this? – stackuser Feb 26 '17 at 4:23
• Yes, since parsing it as ​ not BC ​ instead would presumably give a different answer. ​ ​ ​ ​ – user12859 Feb 26 '17 at 4:26
• Yes that would. – stackuser Feb 26 '17 at 4:32
• The correct answer might be incorrect. It happens. – Yuval Filmus Feb 26 '17 at 4:47

$AB+BC+(\neg B)C=AB+(B+\neg B)C=AB+C$
You can check that also comparing the truth-tables of $AB+BC+(\neg B)C$ and $AB+C$.