# Simplifying Boolean expression.

I have to show that the following expression are equal using the simplification rules:
$$x' y z + x y' z + x y z' + x' y z' + x y' z' + x' y' z = x y' + y z' + z x'$$
But I can only get to:
$$y'z + y'x + x' y z$$ Please let me know what I am doing wrong here. I don't know how to proceed from here.

• Hint: $ab+ab'=a(b+b')=a$. Commented Mar 24, 2018 at 23:36
• The biggest hint is in the RHS of your expression. Collect expressions that have $xy'$, $yz'$ and $zx'$ in common. Then take a look at @Poypoyan's hint.
– an4s
Commented Mar 24, 2018 at 23:39
• Thank you! it worked. For future reference, is there a rule for which inputs should I group together before simplifying? Commented Mar 25, 2018 at 1:27

Use:

$pq + pq'=p$

In other words: look for pairs of terms that have all literals in common except one.

Thus, the first and sixth term simplify to:

$x'yz+x'y'z=x'z$

The second and fifth and also be combined:

$xy'z+xy'z'=xy'$

And finally, the third and fourth:

$xyz'+x'yz'=yz'$

So, the whole thing simplifies to:

$x'z+xy'+yz'$