# Prove This Bool Expression

Prove $x'z+xyz+xy'z=z$ can you show how you solve this using Boolean Algebra.

My main problem is when I do this $xz (y + y') = 1$ So $1$ times $x =$ ?

• $$xz(y+y')=xz$$ and $x'z+xz=z(x'+x)=z$ Nov 10 '13 at 5:33

$$x'z + xyz + xy'z = z$$ $$x'z + xz (y + y') \ // AssociationRule$$ $$x'z + xz * 1 \ // \ a + a' = 1; a * 1 = a$$ $$z (x'+x) \ // \ a + a' = 1$$ $$z * 1 \ // \ a * 1 = a$$ $$z$$
How about simply $$\begin{eqnarray} x'z + xyz + xy'z &=& (x'+xy+xy')z \\ &=&(x'+x(y+y'))z \\ &=&(x'+x)z \\ &=& z, \end{eqnarray}$$ using the distributive laws and $x+x'=1$.