Use DeMorgan’s theorem to remove the complement outside the braces, and make the truth table with...
Use DeMorgan’s theorem to remove the complement outside the braces, and make the truth table with output and all input variables for the following function:
(x+y)’+z’(x’+z)’.
Homework Answers
Truth table with output and all input variables:
| x | y | z | (x+y)' | x'y' | (x'+z)' | xz' | (x+y)' + z'(x'+z)' |
x'y' + z'xz' or x'y' + xz' |
|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
| 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
Therefore, by using DeMorgan’s theorem we get:
(x+y)' + z'(x'+z)' = x'y' + z'xz' = x'y' + xz'
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