# Can $A+\bar{A}\bar{B}+BC$ get any simpler?

I've simplified this Boolean formula quite a bit. Can it get any simpler? My definition of simple in this case is using the least amount of operators (and, or)

Title is "A or (negative A and negative B) or (B and C)"

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I have always found drawing Venn diagrams surprisingly effective for thinking about such expressions. –  Mark Bennet Sep 27 '11 at 21:09
Karnaugh maps may be good approach to the such problems –  pedja Sep 30 '11 at 7:00

$A+\overline{A}\,\overline{B} = (A+\overline{A})(A+\overline{B}) = (A+\overline{B})$. So you can simplify $A+\overline{A}\,\overline{B} + \overline{B}\,\overline{C}$ to $A+\overline{B} + BC$.
Likewise, $\overline{B}+BC = (\overline{B}+B)(\overline{B}+C) = \overline{B}+C$. So the entire thing is equivalent to $A+\overline{B}+C$.
So, minimized formula is: $A\lor \neg B\lor C$