Distributivity of AND/OR in propositional algebra?

Question

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.

Answer 1

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.

Answer 2

I just wanted to mention that the common approach to simplify boolean expressions is the Karnaugh Map, and there are automated tools that could help you with it, such as boolean-algebra.com. If you plug your expression into it (the notation is $BA+C\overline{A}$), you'll see that it generates the following Karnaugh Map, which (as the other answer mentioned) cannot be further simplified with the regular Boolean operations: