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

Question

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)"

Answer 1

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

Answer 2

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.

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