Breaking down expressions using boolean laws for these functions

Question

Just want to make sure I'm understanding the laws correctly. Can I break down the following expressions like so?

F1 = x’y’z’ + x’y’z + x’yz’

F1 = x’y’(z’ + z) + x’yz’

F1 = x’y’(1) + x’yz’

F1 = x’y’ + x’yz’

F1 = x’y’ + x’yz’

---

F2 = x’yz’ + x’yz + xyz’ + xyz

F2 = x’y(z’ + z) + xy(z’ + z)

F2 = x’y + xy

F2 = y(x’+ x)

F2 = y

Answer 1

Your simplifications are fine.

Note that $F_1$ could also have been simplified to: $$x'z' + x'y'z$$ by combining the $y$ and $y'$ instead of the $z$ and $z'$. The observed symmetry in $y$ and $z$ is probably best expressed by: $$x'(yz)'$$