# Karnaugh Graph Simplification

I have following truth Table :

F(w,x,y,z) = Σ(0,2,5,7,8,10,12,13,14);

    Truth Table
W   X   Y   Z   F
0   0   0   0   0   1
1   0   0   0   1   0
2   0   0   1   0   1
3   0   0   1   1   0
4   0   1   0   0   0
5   0   1   0   1   1
6   0   1   1   0   0
7   0   1   1   1   1
8   1   0   0   0   1
9   1   0   0   1   0
10  1   0   1   0   1
11  1   0   1   1   0
12  1   1   0   0   1
13  1   1   0   1   1
14  1   1   1   0   1
15  1   1   1   1   0


With the following Karnaugh Map

  W  X
Y
Z


I'm able to reduce this to the following SOP

 ~x~z + w~z + x~yz + ~wxy


My Professor explicitly told me that this function can be reduced to 2 SOP terms, but he doesn't have the time to demonstrate this as finals start this week.

I want to trust my professor on this, but I do not see how this can be reduced any more than it is.

How to prove that this can be reduced to 2 terms or prove that it can not be reduced to less than 4 ?

Not sure if typo. There is a slight mistake in your solution. $$F = \overline x\overline z + w\overline z + x\overline yz+\overline wxz$$