I read this as ¬P⋂(Q⋃¬R)
In words this is the intersection (AND) of NOT-P and the output of the union (inclusive OR) of Q and NOT-R.
Each of the Boolean variables P, Q, R can each have one of two values 0 or 1, No or Yes, FALSE or TRUE, these binary pairs being equivalent. Using 0 and 1 is the simplest representation so we'll consider all possible inputs:
(PQR)={(000) (001) (010) (011) (100) (101) (110) (111)} and their 8 corresponding outputs. The columns of the truth table give progressive stages in the evaluation of the expression.
| 1 |
2 |
3 |
4 |
5 |
6 |
7 |
| P |
Q |
R |
¬P |
¬R |
(Q⋃¬R) |
¬P⋂(Q⋃¬R) |
| 0 |
0 |
0 |
1 |
1 |
1 |
1 |
| 0 |
0 |
1 |
1 |
0 |
0 |
0 |
| 0 |
1 |
0 |
1 |
1 |
1 |
1 |
| 0 |
1 |
1 |
1 |
0 |
1 |
1 |
| 1 |
0 |
0 |
0 |
1 |
1 |
0 |
| 1 |
0 |
1 |
0 |
0 |
0 |
0 |
| 1 |
1 |
0 |
0 |
1 |
1 |
0 |
| 1 |
1 |
1 |
0 |
1 |
0 |
0 |
Column 7 is the final output, that is, evaluation of the given Boolean expression.
The unary NOT operator simply changes 0 to 1 or 1 to 0. Columns 4 and 5 show this operator applied to P and R.
The truth table for the binary operator OR:
| Input 1 ꜜ Input 2→ |
0 |
1 |
| 0 |
0 |
1 |
| 1 |
1 |
1 |
The truth table for the binary operator AND:
| Input 1 ꜜ Input 2→ |
0 |
1 |
| 0 |
0 |
0 |
| 0 |
0 |
1 |