T¬Tet(a)
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How it works
Connectives build bigger sentences out of smaller ones. The truth of the whole depends only on the truth of the parts, which is why a small truth table covers every case.
∨ is inclusive. Cube(a) ∨ Small(a) is true when a is a small cube, too. English “or” sometimes means “one or the other but not both”; logic’s ∨ never does.
| P | Q | ¬P | P ∧ Q | P ∨ Q |
|---|---|---|---|---|
| T | T | F | T | T |
| T | F | F | F | T |
| F | T | T | F | T |
| F | F | T | F | F |
Worth memorizing
¬ flips true and false.
¬¬Cube(a) says the same thing as Cube(a).
∧ is true only when both sides are true.
∨ is true when at least one side is true.
Both true still counts.
Practice
0 of 4 rightQuestion 1¬Large(a)
Question 2Cube(a)∧Tet(b)
Question 3Small(b)∨Dodec(b)
Question 4¬(Small(a)∧Small(c))