22. Smith (X) is passing (Y). No one I know (Z) is passing (Y). No one I know (Z) is Smith (X). Valid. The negative conclusion is matched by the negative second premise; the two distributed terms in the conclusion (Z and X) are both distributed in the premises; and the middle term (Y) is distributed in the second premise.

23. Some students (X) are rockers (Y). No old people (Z) are rockers (Y). Therefore, no old people (Z) are students (X). Invalid. The difference between this argument and the previous two is in the first word: this is a non-universal syllogism. And, as a result, it violates the rule that a distributed term in the conclusion (X) must be distributed in the premise.

24. All good (X) are big (Y). Some Spartans (Z) are not big (Y). Therefore, some Spartans (Z) are not good (X). Valid. The negative conclusion is matched by the negative second premise; the distributed term in the conclusion (X) is distributed in the first premise; and the middle term (Y) is distributed in the second premise.

25. Some doctors (X) are not watchers (Y). Jessica (Z) is a doctor (X). Therefore, Jessica (Z) is not a watcher (Y). Invalid. The middle term (X) is not distributed in either premise.

26. Some bad (X) are expelled (Y). No I (Z) am bad (X). No I (Z) am expelled (Y). Invalid. One of the terms distributed in the conclusion (Y) is not distributed in the premise.

27. All snobs (X) are a waste (Y). Some girls (Z) are not snobs (X). Therefore, some girls (Z) are not a waste (Y). Invalid. One of the terms distributed in the conclusion (Y) is not distributed in the premise.

28. Some grapes (X) are green (Y). No strawberries (Z) are green (Y). Therefore, some grapes (X) are not strawberries (Z). Valid. The negative conclusion is matched by the negative second premise; the distributed term in the conclusion (X) is distributed in the first premise; and the middle term (Y) is distributed in the second premise.

29. All cherries (X) are red (Y). Some apples (Z) are not red (Y). So no cherry (X) is an apple (Z). Invalid. One of the terms distributed in the conclusion (Z) is not distributed in the premise.

30. All green (X) are sour (Y). Some apples (Z) are green (X). Some apples (Z) are sour (Y). Valid: there are no negatives or distributed terms in the premise, and the middle term (X) is distributed in the second premise.

31. Some motorcycles (X) are loud (Y). Harleys (Z) are loud (Y). Therefore, Harleys (Z) are motorcycles (X). Invalid: the middle term (Y) is not distributed in either premise.

32. All long (X) are cute (Y). Some cats (Z) are not long (X). Therefore, some cats (Z) are not cute (Y). Note that the argument requires us to accept "short" as equivalent to "not long," which it is not. But even if we ignore that problem, the argument is still invalid, because the distributed term in the conclusion (Y) is not distributed in the first premise.

33. Some long books (X) are hard (Y). War and Peace (Z) is long (X). Therefore, War and Peace (Z) is hard (Y). Invalid: the middle term (X) is not distributed in either premise.

34. Some alcoholics (X) are irresponsible (X). No irresponsible (Y) should be a cop (Z) Therefore, some alcoholics (X) should not be cops (Z). Valid: the negative conclusion is matched by a negative second premise; the distributed term in the conclusion (Z) is distributed in the second premise; and the middle term (Y) is distributed in the second premise.

35. Some workers (X) are earners (Y) Some students (Z) are not workers (X). Therefore, some students (Z) are not earners (Y). Invalid: the distributed term in the conclusion (Y) is not distributed in the first premise.

36. If movies (P) => no party (Q). Party = Not "no party" (Not Q) Therefore, no movies (Not P). Valid: negating the consequent.

37. If unwell (P) => not play (Q). Playing = Not "not play" (Not Q). Therefore, Not unwell (Not P). The above argument seems to be valid, but there is a problem. The conclusion is supposed to be "feels fine" but the best we can deduce is Mary is "not unwell." And there is a range of possibilities between feeling fine and not unwell. The conclusion that she "feels fine," therefore, is invalid.

38. If L.A. (P) => London (Q). Not London (Not Q). Therefore, Not L.A. (Not P). Valid: negating the consequent.

39. If prescribe (P) => psychiatrist (Q). Not psychiatrist (Not Q). Therefore, not prescribe (Not P). Valid: negating the consequent.

40. If after one (P) => late (Q). If late (Q) => skip (R). If skip (R) => groggy (S). Groggy (S) . . . invalid. Affirming the consequent.