Mathematical Proof/Appendix/Answer Key/Mathematical Proof/Introduction/Logical Reasoning
1.1, Logical Reasoning.
These are the answers to the exercises in section 1.1, Logical Reasoning
- Truth tables
| P | Q |  |
 |
|---|---|---|---|
| T | T | F | T |
| T | F | F | T |
| F | T | T | T |
| F | F | T | F |
| P | Q |  |
 |
|---|---|---|---|
| T | T | F | F |
| T | F | T | T |
| F | T | F | T |
| F | F | T | T |
| P | Q | R |  |
 |
|---|---|---|---|---|
| T | T | T | T | T |
| T | T | F | T | F |
| T | F | T | T | T |
| T | F | F | T | F |
| F | T | T | T | T |
| F | T | F | T | F |
| F | F | T | F | T |
| F | F | F | F | T |
| P | Q | R | S |  |
 |
 |
|---|---|---|---|---|---|---|
| T | T | T | T | T | T | T |
| T | T | T | F | T | T | T |
| T | T | F | T | T | T | T |
| T | T | F | F | T | F | F |
| T | F | T | T | F | T | T |
| T | F | T | F | F | T | T |
| T | F | F | T | F | T | T |
| T | F | F | F | F | F | T |
| F | T | T | T | F | T | T |
| F | T | T | F | F | T | T |
| F | T | F | T | F | T | T |
| F | T | F | F | F | F | T |
| F | F | T | T | F | T | T |
| F | F | T | F | F | T | T |
| F | F | F | T | F | T | T |
| F | F | F | F | F | F | T |
| P | Q | R | S |  |
 |
 |
|---|---|---|---|---|---|---|
| T | T | T | T | T | T | T |
| T | T | T | F | T | F | T |
| T | T | F | T | T | T | T |
| T | T | F | F | T | T | T |
| T | F | T | T | F | T | F |
| T | F | T | F | F | F | T |
| T | F | F | T | F | T | F |
| T | F | F | F | F | T | F |
| F | T | T | T | T | T | T |
| F | T | T | F | T | F | T |
| F | T | F | T | T | T | T |
| F | T | F | F | T | T | T |
| F | F | T | T | T | T | T |
| F | F | T | F | T | F | T |
| F | F | F | T | T | T | T |
| F | F | F | F | T | T | T |
2. Negated statements
