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2. If sleep (P) => not tired (Q). Not sleep (Not P) . . . invalid. Negating the antecedent.

3. If coffee (P) => awake (Q) No coffee (Not P) . . . invalid. Negating the antecedent.

4. If page (P) => need ride (Q) No page (Not P) . . . invalid. Negating the antecedent.

5. Notice the double "All": All Car owners (X) are school drivers (Y) All SJSU (Z) are car owners (X) So, all SJSU (Z) are school drivers (Y). Valid. No negative in the conclusion; Z is distributed in the conclusion and the second premise; and the middle term (X) is distributed in the first premise.

6. If guilty (P) => jail (Q) Jail (Q) . . . invalid. Affirming the consequent.

7. Only if: If go out (P) => birthday (Q) Not go out (Not P) . . . invalid. Negating the antecedent.

8. If lose (P) => exercise or eat less (Q) In the case of an "or," both must be negated, and this only negates one, so "not eat less" cannot be "Not Q." Therefore, invalid.

9. If >50% (P) => secede (Q) 49.5% = Not >50% = Not P . . . invalid. Negating the antecedent.

10. All speeders (X) are ticket receivers (Y) I (Z) am a ticket receiver (Y) . . . invalid. The middle term (Y) is not distributed in either premise, confirming the invalidity. Note: this doesn't say that CHP did not give tickets to reckless drivers, too, only that they did give them to all the speeders.

11. All nice (X) are saints (Y). Some do-gooders (Z) are not nice (X). Therefore, some do-gooders (Z) are not saints (Y). Invalid: Y is distributed in the conclusion, but not in the first premise.

12. All men (X) are jerks (Y). No woman (Z) is a man (X) . . . invalid form ("No Z is Y" would be valid). In the suggested conclusion, "No woman is a jerk," the term "jerk" is distributed in the conclusion, but not in the first premise, confirming the invalidity.

13. The problem here is not with the form, which is valid, but with the inconsistent use of the word "light." When we say, aluminum is "light," we mean it has a relatively low density (that is, a low weight for its volume). But when we say that a bike frame is light, we mean that it doesn't weigh much; how much a bike frame weighs would depend on design as much as materials. So a solid frame, or a very large or thick frame, might be heavy even if it were made of light material like aluminum.

14.All happy (X) are comfortable (Y). Some comfortable (Y) are expensive (Z). Therefore, all happy (X) are expensive (Z). Invalid: the middle term (Y) is not distributed.

15. All athletes (X) are healthy (Y) No sick people (Z) are healthy (Y). So no sick people (Z) are athletes (X). Valid. The negative conclusion is matched by the second negative premise; the two distributed terms in the conclusion (Z and X) are distributed in the premises; and the middle term (Y) is distributed in the second premise.

16. Some students (X) are not-working (Y). Some students (X) are passing (Z). Therefore, some not-working (Y) are passing (Z). Invalid: the middle term (X) is not distributed.

17. If 2/3 (P) => pass (Q). Not 2/3 = Not P . . . invalid. Since the argument is invalid, you cannot conclude anything. So the bill may have passed, or it may have failed. Think of it this way: nothing was said about what would happen if the vote was less than two-thirds, only about what would happen if the vote was two-thirds or more.

18. If 3 of 4 (P) => pass (Q). Not 3 of 4 = Not P . . . invalid. Since the argument is invalid, you cannot conclude anything. You may have passed, or you may have failed.

19. All patients (X) are eligible (Y). Some children (Z) are patients (X). Therefore, some children (Z) are eligible (Y). Valid: there is no negative or distributed term in the conclusion, and the middle term (X) is distributed in the first premise.

20. If <15 (P) => canceled (Q) Not canceled (Not Q). Therefore, not <15 (Not P). The argument above is valid, but there's a difference between "not less than 15" and "more than 15." In this case, you cannot conclude that there are more than 15 students enrolled, because there may be 15 exactly.