F T T T F √ 16. Valid. Let = and = E Eddie can vote, R he (Eddie) is registered. E R E R R / E ≡ F T F T F Since the only way to get the conclusion false is for to be false, and the only way to get the second E premise true is for R to be true, it will be impossible to then get the first premise true. Thus, the argument is valid. Valid. Let = and = 17. E Eddie can vote, R he (Eddie) is registered. E R E R E / R ≡ T F F T F Since the only way to get the conclusion false is for to be false, and the only way to get the second R premise true is for to be true, it will be impossible to then get the first premise true. Thus, the argument E is valid. 18. Let = and = E Eddie can vote, R he (Eddie) is registered. E R E ≡ R ~ R / ~ E T F F T F 19. Let = and = E Eddie can vote, R he (Eddie) is registered. E R E R ~ E / ~ R ≡ F T F T F Since the only way to get the conclusion false is for to be true, and the only way to get the second R premise true is for to be false, it will be impossible to then get the first premise true. Thus, the argument E is valid. 20. Valid. Let = and L Linda can think, C = she (Linda) is conscious. L C L C C L ≡ F T F T F Since the only way to get the conclusion false is for L to be false, and the only way to get the second premise true is for to be true, it will be impossible to then get the first premise true. Thus, the argument C is valid.
F T T T F √ 16. Valid. Let E = Eddie can vote, and R = he (Eddie) is registered. E R E ≡ R R / E F T F T F Since the only way to get the conclusion false is for E to be false, and the only way to get the second premise true is for R to be true, it will be impossible to then get the first premise true. Thus, the argument is valid. 17. Valid. Let E = Eddie can vote, and R = he (Eddie) is registered. E R E ≡ R E / R T F F T F Since the only way to get the conclusion false is for R to be false, and the only way to get the second premise true is for E to be true, it will be impossible to then get the first premise true. Thus, the argument is valid. 18. Let E = Eddie can vote, and R = he (Eddie) is registered. E R E ≡ R ~ R / ~ E T F F T F 19. Let E = Eddie can vote, and R = he (Eddie) is registered. E R E ≡ R ~ E / ~ R F T F T F Since the only way to get the conclusion false is for R to be true, and the only way to get the second premise true is for E to be false, it will be impossible to then get the first premise true. Thus, the argument is valid. 20. Valid. Let L = Linda can think, and C = she (Linda) is conscious. L C L ≡ C C L F T F T F Since the only way to get the conclusion false is for L to be false, and the only way to get the second premise true is for C to be true, it will be impossible to then get the first premise true. Thus, the argument is valid.
AnswersChapter7.docx