I have to minimize a function without using Karnaugh maps, but only the theorems and laws of boolean algebra.
F(x,y,z) = (NOT Y AND NOT Z) OR (NOT X AND Y) OR (NOT X AND Y AND Z) OR (X AND Y AND NOT Z)


Alternative notations:

F(x,y,z) = (y ∧ z) ∨ (x ∧ y) ∨ (x ∧ y ∧ z) ∨ (x ∧ y ∧ z)

F(x,y,z) = !y * !z + !x * y + !x*y*z + x*y*!z


According to Wolframalpha, the result should be: (X ∧ Y)∨ Z. Unfortunately, it doesn't show a step by step solution for these kind of problems...