| 1. | Suppose you know that a certain argument is valid but do not know whether its premises and conclusion are true or false. If you are given one of the further items of information a-c about the premises of the argument, what if anything can you say about the truth value of its conclusion? | |
| a. | The premises are all true. | |
| b. | The premises are all false. | |
| c. | Some premises are true and some are false. | |
| 2. | Suppose that φ, ψ / χ is an argument that you know to be valid. If you find that the conclusion χ is false, what if anything can you say about the truth values of the premises φ and ψ? |
| 3. | For each of the following items of information, tell what you can conclude from it about the equivalence of sentences φ and ψ. | |
| a. | φ and ψ are both true | |
| b. | φ and ψ are both false | |
| c. | φ is true and ψ is false | |
| d. | There is a sentence χ such that χ and φ together entail ψ, and χ and ψ together entail φ (i.e., χ, φ ⇒ ψ and χ, ψ ⇒ φ) | |
| 4. | For each of the following pieces of information, tell what if anything you can conclude about the possibilities left open and the possibilities ruled out by the sentence φ: | |
| a. | φ is equivalent to a tautology ψ | |
| b. | φ entails ⊤ | |
| c. | a tautology ψ entails φ | |
| d. | φ is equivalent to ⊥ | |
| e. | φ entails an absurdity ψ | |
| f. | ⊥ entails φ | |