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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
up vote 7 down vote accepted

$A+\overline{A}\,\overline{B} = (A+\overline{A})(A+\overline{B}) = (A+\overline{B})$. 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 $A+\overline{B}+C$.

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If you make Karnaugh map for this expression you will get map as it is shown on the picture bellow.Now you have to find maximal possible groups of ones and you will get minimized disjunctive form of the formula.

enter image description here

So, minimized formula is: $ A\lor \neg B\lor C$

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