Homework SourseGiven the function Fx y z yxz xz xyz yz List the truth t
Given the function, F(x, y, z) = y(x\'z = xz\') + x(yz + yz\') List the truth table for F.
Solution
X
Y
Z
X’
Z’
X’Z
XZ’
X’Z+XZ’
Y(X’Z+XZ’)
YZ
YZ’
YZ+YZ’
X(YZ+YZ’)
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
F(X,Y,Z) = Y(X\'Z+XZ\') +X(YZ+YZ\')
= X\'YZ + XYZ\' +XYZ
| X | Y | Z | X’ | Z’ | X’Z | XZ’ | X’Z+XZ’ | Y(X’Z+XZ’) | YZ | YZ’ | YZ+YZ’ | X(YZ+YZ’) |
| 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
| 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 |
