Read these sections to learn how to interpret, make, and apply truth tables to sentential logic formulas, note conditional statements in sentential logic, and translate the word "unless" into sentential logic. Be sure to note the difference between an antecedent and a consequent and between a necessary and sufficient condition.
Complete the exercises, checking your answers against the key.
| A | B | C | (A v B) · (A v C) |
~A |
B v C |
|---|---|---|---|---|---|
| T | T | T | T T T |
F | T |
| T | T | F | T T T |
F | T |
| T | F | T | T T T | F | T |
| T | F | F | T T T | F | F |
| F | T | T | T T T | T | T |
| F | T | F | T F F | T | T |
| F | F | T | F F T | T | T |
| F | F | F | F F F | T | F |
| R | T | S | R · (T v S) |
T |
~S |
|---|---|---|---|---|---|
| T | T | T | T T |
T | F |
| T | T | F | T T |
T | T |
| T | F | T | T T |
F | F |
| T | F | F | F F |
F | T |
| F | T | T | F T |
T | F |
| F | T | F | F T |
T | T |
| F | F | T | F T | F | F |
| F | F | F | F F | F | T |
| A | B | ~(A v B) |
~A v ~B |
|---|---|---|---|
| T | T | F T |
F F F |
| T | F | F T |
F T T |
| F | T | F T |
T T F |
| F | F | T F |
T T T |
| D | R | S | (R v S) · ~ D |
~ R |
S · ~ D |
|---|---|---|---|---|---|
| T | T | T | T F F |
F | F |
| T | T | F | T F F |
F | F |
| T | F | T | T F F |
T | F |
| T | F | F | F F F |
T | F |
| F | T | T | T T T |
F | T |
| F | T | F | T T T |
F | F |
| F | F | T | T T T | T | T |
| F | F | F | F F T |
F | F |