How can I rewrite something like (B AND A) OR (C AND NOT(A))? I understand that if I have something like (B AND A) OR (C AND A), I can rewrite it as A AND (B OR C), but I'm not sure what to do if one of them is negated.
Distributivity of AND/OR in propositional algebra?
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logic
propositional-calculus
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1You might want to use the logical symbols $\land$ (AND), $\lor$ (OR), $\neg$ (NOT) to make your question more readable. As for your the answer, there is not really a shorter way to write as you did. – 2017-02-28
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There's no standard notation in logic that will let you write this formula any simpler.
Many programming languages have an if-then-else operator that would allow you to write something like if A then B else C or A ? B : C, and in digital logic the functionality is that of a basic 2-way multiplexer gate.
But there is no tradition for working with such connectives in mathematical logic.