1.4 KiB
1.4 KiB
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Boolean functions
An example of a Boolean function:
f(x,y,z) = (x \land y) \lor (\lnot(x) \land z )
Here is a work through where f(1, 0, 1):
- The first disjunction :
\lnot(x) \land zis false becausexis 1 andzis 0 - The second disjunction:
x \land yis false becausexis 1 andyis 1 - The overall function returns false because the main connective is disjunction and both of its disjuncts are false
We can compute all possible outputs of the function by constructing a trkjuth table with each possible variable as the truth conditions and the output of the function as the truth value:
x |
y |
z |
f(x,y,z) = (x \land y) \lor (\lnot(x) \land z ) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 |