# Boolean Algebra - Minimization

I have a problem with this assignment:

The 26th one:

I am supposed to minimize this, and I get to

" XY + ZY + ( Z*(inverted X) )"

But solution to this problem is

I don't know how to minimize more the solution I got up there :/

Does anyone know?

See if this makes sense... z+y goes away because the OR function is handled by the other two that have those inputs. Best way to do this is draw a K-map. I used xy on the vertical axis, and z on the horizontal and the equation (x+z)(!x+y) was obvious.
Then, because you expand that equation to (!xx) + (!xz) + (zy) + (xy) and notice that (!xx) has no contribution, and you create another K-map for the remaining terms (excluding (!xx)) the equation (xy) + (!xz) becomes obvious.
• How about... !xz + !!z + !!y + xy = !x(z+z) + x(y+y) = !xz+xy Assuming, I applied that DeMorgan's identity correctly for the zy term... I dunno, could be crap-math :/ – CapnJJ Aug 28 '18 at 18:40
• zy = (!!z+!!y) – CapnJJ Aug 30 '18 at 15:56