Here are some exercises you can practice on:
1. P ≡ ~N // N v P
2. K ≡ ~L / ~(L ∙ ~K) // K ⊃L
3. Z // E ⊃ (Z ⊃ E)
4. C ≡ D / E v ~D // E ⊃ C
5. A ⊃ (B v C) / ~C v B // A ⊃ B
6. J ⊃ (K ⊃ L) / K ⊃ (J ⊃ L) // (J v K) ⊃ L
7. If Sartre’s an existentialist, then Wittgenstein wrote the Tractatus, therefore if Wittgenstein wrote the Tractatus, Sartre’s an existentialist.
S ⊃ W // W ⊃ S
8. Hurley is President, so either he’s President or Ackermann is Dean.
H// H v A
9. If “time flies” is a metaphor, it’s not literally true. If it’s not literally true then time does not fly, so if “time flies” is a metaphor, then time does not fly.
F ⊃ ~T/ ~T ⊃ ~R // F ⊃ ~R
10. If the argument from design is weak, it’s a weak analogy. In order to be a weak analogy, it must make an unwarranted comparison, so the argument from design makes an unwarranted comparison.
D ⊃ A / A ⊃ ~W // ~W
11. Winters are cold and summers are hot, so either summers are hot or the moon is made of green cheese.
W ∙ S // S v M
12. Russell was either a realist or an empiricist. If the former, then he was not an idealist, so he was not an empiricist.
R v E/ R ⊃ ~I // ~E
13. If he loves her, he’ll marry her. Therefore if he doesn’t love her he won’t marry her.
L ⊃ M // ~L ⊃ ~M
14. If humans can settle on the moon, then they can settle on Mars. If they can settle on Mars, they can settle on Jupiter. So if the moon can be settled, so can Jupiter.
M ⊃ A / A ⊃ J // M ⊃ J
15. This argument is invalid if and only if it can have true premises and a false conclusion. Therefore it is invalid, since it has a false conclusion.
~V ≡ (T ∙ F) / F // ~V
16. The fact that animals are less intelligent than us does not imply that we may disregard their welfare. If we disregard their welfare, then we are inhumane, and no better than animals ourselves. Thus, if we disregard their welfare, it is false that they are less intelligent than us.
~(L ⊃ D) / D ⊃ (~H ∙ ~B) // D ⊃ ~L
17. If Sweden is in North Africa, then either Egyptians are blue-eyed or Swedes are dark and handsome. Sweden is not in North Africa, so Egyptians are not blue-eyed.
S ⊃ (E v (D ∙ H)) / ~S // ~E
18. Unless you have both a sledge and a wedge, you are not going to be splitting any wood. You have a sledge but you don’t have a wedge, so either you’re not going to be splitting any wood or else you’re going to go buy one.
(S ∙ W) v ~Y / S ∙ ~W // ~Y v B
19. If she loves him, she’ll marry him, therefore if she doesn’t marry him, she doesn’t love him.
L ⊃ M // ~M ⊃ ~L
This pdf shows you the truth tables for 4 and 6, and for 14-19.