Help on Boolean Expression Simplification

Question

I got a question and I'm wondering is the way I solve it correct? $$xyz + x'z' + xyz' + x'y'z + x'yz'$$ $$= xyz + xyz' + x'y'z + x'yz' + x'yz' + x'y'z'$$ $$= xyz + xyz' + x'y'z + x'yz' + x'y'z'$$ $$= xy + x'y' + x'yz'$$

Answer 1

You did everything correct, but there is one more simplification you can make from your third step on:

$$xyz + xyz' + x'y'z + x'yz' + x'y'z'$$ (and now create a copy of $x'y'z'$)

$$xyz + xyz' + x'y'z + x'y'z' + x'yz' + x'y'z'$$

$$xy + x'y' + x'z'$$

You can also combine the last two terms to $x'(y'+z')$, and you can do some DeMorgan's as well to further minimise the number of operations, but if it has to be in CNF (SOP), then stick to the last line as is.

Answer 2

Your input expression gives:

 x | y | z | xyz | x'z' | xyz' | x'y'z | x'yz' | xyz+x'z'+xyz'+x'y'z+x'yz'
---|---|---|-----|------|------|-------|-------|---------------------------
 0 | 0 | 0 |  0  |  1   |  0   |   0   |   0   |              1
 0 | 0 | 1 |  0  |  0   |  0   |   1   |   0   |              1
 0 | 1 | 0 |  0  |  1   |  0   |   0   |   1   |              1
 0 | 1 | 1 |  0  |  0   |  0   |   0   |   0   |              0
 1 | 0 | 0 |  0  |  0   |  0   |   0   |   0   |              0
 1 | 0 | 1 |  0  |  0   |  0   |   0   |   0   |              0
 1 | 1 | 0 |  0  |  0   |  1   |   0   |   0   |              1
 1 | 1 | 1 |  1  |  0   |  0   |   0   |   0   |              1

Your output expression gives:

 x | y | z | xy | x'y' | x'yz'| xy+x'y'+x'yz'
---|---|---|----|------|------|---------------
 0 | 0 | 0 | 0  |  1   |  0   |       1
 0 | 0 | 1 | 0  |  1   |  0   |       1
 0 | 1 | 0 | 0  |  0   |  1   |       1
 0 | 1 | 1 | 0  |  0   |  0   |       0
 1 | 0 | 0 | 0  |  0   |  0   |       0
 1 | 0 | 1 | 0  |  0   |  0   |       0
 1 | 1 | 0 | 1  |  0   |  0   |       1
 1 | 1 | 1 | 1  |  0   |  0   |       1

As you can see, they (the right-most columns) are identical.

Answer 3

One further simplification: x'y'+y(x+z')