93 Truth Table Completion
Logic
Boolean Algebra
Truth Tables
Logical Operators
Propositional Logic
93.1 Description:
This task involves completing truth tables for given logical expressions to evaluate the model’s understanding of Boolean logic and its ability to determine the truth value of complex statements.
93.2 Modality:
Text only
93.3 Examples:
93.3.1 Example 1:
Input:
Complete the truth table for the logical expression: (P AND Q) OR (NOT P)Output:
| P | Q | P AND Q | NOT P | (P AND Q) OR (NOT P) |
|---|---|---------|-------|----------------------|
| T | T | T | F | T |
| T | F | F | F | F |
| F | T | F | T | T |
| F | F | F | T | T |
Explanation: We evaluate each subexpression for all possible combinations of P and Q, then combine them according to the main expression.93.3.2 Example 2:
Input:
Complete the truth table for the logical expression: P XOR QOutput:
| P | Q | P XOR Q |
|---|---|---------|
| T | T | F |
| T | F | T |
| F | T | T |
| F | F | F |
Explanation: XOR (exclusive or) is true when P and Q have different truth values, and false when they have the same truth value.