| 1. | Restate, with unrestricted quantifiers, the generalizations below that employ restricted quantifiers—and vice versa. Write out English readings for the results. | |
| a. | (∀x: Fx) Gx | |
| b. | ∀x (Fx → ¬ Gx) | |
| c. | (∀x: Fx ∧ ¬ Gx) Hx | |
| d. | ∀x ((Px ∧ ¬ Rxx) → Rxa) | |
| e. | (∀x: Rxa ∧ ¬ Rbx) ¬ (Fx ∨ Gx) | |
| f. | ∀x ((Fx ∨ Gx) → (Hx ∧ ¬ Kx)) | |
| 2. | Analyze the following in as much detail as possible, stating the resulting form using both restricted and unrestricted quantifiers: | |
| a. | Everyone had heard about the accident. | |
| b. | Every relative of Sam agreed with him about the issue. | |
| c. | Edna took pleasure in none of her possessions. | |
| d. | Tom found only empty boxes | |
| e. | The survey was sent to all members of the organization except its officers. | |
| f. | Only countries bordering the Pacific will prosper. | |
| 3. | State in idiomatic English the generalizations that could be represented symbolically by the following: | |
| a. | (∀x: x is a dog) x chases cats. | |
| b. | (∀x: x is a hole) Holly patched x. | |
| c. | (∀x: x is a person) ¬ x volunteered. | |
| d. | (∀x: ¬ x is a cockroach) ¬ x will survive. | |
| e. | ∀x ¬ x seemed right. | |
| f. | (∀x: x was a reviewer ∧ ¬ x was a friend of the director) x panned the movie. | |
| g. | (∀x: x is a bird ∧ ¬ x is an early bird) ¬ x gets a worm. | |
| h. | (∀x: ¬ x is a small child) the movie bored x. | |