Quiz: Chapter 7 - Logical Reasoning

1 If all roses are flowers and some flowers fade quickly, which statement must be true?

All roses fade quickly Some roses fade quickly No roses fade quickly Some roses do not fade quickly

2 All scientists are researchers. Some researchers are professors. Which conclusion follows?

All professors are scientists Some professors may be scientists No scientists are professors All researchers are professors

3 No birds are mammals. All bats are mammals. What can be deduced?

Some bats are birds No bats are birds All birds are bats Some birds are bats

4 If some A are B and all B are C, which is certain?

All A are C Some A are C No A are C Some C are not A

5 In a Venn diagram with two overlapping circles A and B, the overlapping area represents:

Only A Only B Both A and B Neither A nor B

6 All X are Y. No Y are Z. What must be true?

Some X are Z No X are Z All Z are X Some Z are X

7 If "Some doctors are surgeons" is true, which must be false?

All surgeons are doctors No doctors are surgeons Some surgeons are not doctors All doctors are surgeons

8 Premise 1: All P are Q. Premise 2: Some Q are R. Conclusion: Some P are R. Is this valid?

Yes, necessarily true Yes, possibly true No, possibly true No, necessarily false

9 Which syllogism is valid?

All A are B. All C are A. Therefore, all C are B Some A are B. Some B are C. Therefore, some A are C No A are B. No B are C. Therefore, no A are C All A are B. Some A are C. Therefore, all B are C

10 If "No politicians are honest" is false, what must be true?

All politicians are honest Some politicians are honest No honest people are politicians Some politicians are not honest

11 In a family tree, if A is B's mother and B is C's father, then A is C's:

Grandmother Aunt Sister Mother

12 All books in this library are nonfiction. Some old books are fiction. Therefore:

Some old books are not in this library All old books are in this library No old books are nonfiction Some fiction is in this library

13 If "Some X are not Y" is true, which must be false?

All X are Y Some X are Y No X are Y Some Y are not X

14 Which Venn diagram correctly represents "Some A are B and no B are C"?

Two overlapping circles A&B, with B completely separate from C Three circles all overlapping Circle A inside B, B separate from C Circle B inside A, overlapping with C

15 Premise: Only graduates can apply. Conclusion: If someone applied, they must be a graduate. This is:

Valid deduction Invalid generalization Circular reasoning False dilemma

16 All philosophers are thinkers. Some thinkers are writers. Therefore:

Some writers are philosophers No writers are philosophers All thinkers are writers None of the above necessarily follows

17 If "Whenever it rains, the ground gets wet" is true, what follows from "The ground is not wet"?

It is not raining It might be raining The ground never gets wet The rain is light

18 Which is the logical equivalent to "All successful people work hard"?

No unsuccessful people work hard Some hard workers are successful If not working hard, then not successful Only successful people work hard

19 In a syllogism, the middle term must:

Appear in both premises but not conclusion Appear in the conclusion only Be the subject of both premises Be distributed at least once

20 If "No A are B" and "All C are B", what is true about A and C?

Some A are C No A are C All A are C Some C are A

21 Which statement contradicts "Some athletes are not professionals"?

All athletes are professionals Some professionals are athletes No professionals are athletes Some athletes are professionals

22 Three statements: 1) All X are Y. 2) Some Y are Z. 3) Some Z are X. If 1 & 2 are true, then 3 is:

Necessarily true Possibly true Necessarily false Invalid structure

23 If "Only A are B" is true, which must be false?

Some non-A are B All A are B Some A are not B No B are A

24 Which syllogism form is invalid?

All A are B. All B are C. Therefore all A are C No A are B. All C are A. Therefore no C are B Some A are B. All B are C. Therefore some A are C All A are B. Some C are A. Therefore all C are B

25 If "Some A are not B" and "All B are C", what can we conclude?

Some A are not C No A are C All C are A No valid conclusion possible

26 In deductive reasoning, a sound argument requires:

True premises and valid form Persuasive conclusion Many supporting examples Complex logical structure

27 Which Venn diagram represents "Some A are B and some B are not A"?

Two circles perfectly overlapping Circle A entirely within circle B Two circles partially overlapping Two separate circles

28 If "All philosophers are thinkers" and "Socrates is a philosopher", what follows?

Socrates is a thinker All thinkers are philosophers Socrates is not a thinker None of these

29 Which is the contrapositive of "If it's a bird, then it can fly"?

If it can fly, then it's a bird If it's not a bird, then it can't fly If it can't fly, then it's not a bird Only birds can fly

30 What is the logical flaw in "All cats are animals. All dogs are animals. Therefore, all cats are dogs"?

Undistributed middle Illicit major Affirming the consequent False premise

31 If "No P are Q" and "Some R are Q", then:

Some R are not P All R are P No R are P Some P are R

32 Which represents immediate inference from "All S are P"?

No S are P Some S are P Some S are not P All P are S

33 What is the term for "All A are B. All A are C. Therefore, some B are C"?

Valid syllogism Existential fallacy Illicit minor Undistributed middle

34 If "Only if P then Q" is true, what else must be true?

If Q then P If not P then not Q If P then Q Only Q if P

35 Which statement is logically equivalent to "Not all students passed"?

All students failed Some students did not pass No students passed Some students passed

36 In a valid syllogism, if the conclusion is negative:

One premise must be negative Both premises must be negative No premises can be negative The major premise must be universal

37 If "Whenever X occurs, Y follows" is true, and Y didn't occur, then:

X did not occur X might have occurred Y will never occur The premise is false

38 Which correctly analyzes "All A are B. Some B are C. Therefore, some A are C"?

Valid Invalid - undistributed middle Invalid - illicit major Invalid - existential fallacy

39 If "Some X are Y" and "No Y are Z", what follows about X and Z?

Some X are not Z No X are Z All X are Z No valid conclusion

40 What is the immediate inference from "No S are P"?

No P are S Some S are P All S are P Some S are not P

41 Which Venn diagram represents "All A are B, and some B are not A"?

Circle A entirely within circle B Two separate circles Two circles partially overlapping Circle B entirely within circle A

42 If "Only A are B" and "Some C are B", then:

Some C are A All C are A No C are A Some A are not C

43 Which syllogism rule is violated in: "All A are B. All C are B. Therefore, all A are C"?

Undistributed middle Illicit major Negative conclusion Existential fallacy

44 The statement "All A are B" has how many distributed terms?

0 1 2 3

45 If "Some A are not B" is true, which must be false?

No A are B All B are A Some A are B All A are B

46 Which correctly represents "No A are B" in predicate logic?

∀x (Ax → ¬Bx) ∃x (Ax ∧ ¬Bx) ∀x (¬Ax ∨ Bx) ∃x (¬Ax ∧ Bx)

47 If "Whenever P is true, Q is true" and "Q is false", then:

P is false P is true Q is sometimes true P and Q are unrelated

48 Which is the obverse of "All S are P"?

No S are non-P Some S are P No P are S All non-P are non-S

49 In a valid syllogism, how many times must the middle term be distributed?

At least once Exactly once Twice Never

50 If "All A are B" and "Some B are not C", then:

Some A are not C No A are C All A are C No valid conclusion

51 Which represents the logical form of "No mammals are reptiles. All whales are mammals. Therefore, no whales are reptiles"?

All A are B. All C are A. Therefore, all C are B No A are B. All C are A. Therefore, no C are B Some A are B. All C are A. Therefore, some C are B No A are B. Some C are A. Therefore, no C are B

52 If "Some A are B" and "All B are C", which must be true?

Some A are C All A are C No A are C Some C are not A

53 Which is the converse of "No S are P"?

No P are S Some S are not P All S are non-P Some P are not S

54 If "All philosophers are thinkers" and "No thinkers are irrational", then:

No philosophers are irrational Some philosophers are irrational All thinkers are philosophers Some irrational people are philosophers

55 Which represents "Some S are not P" in predicate logic?

∃x (Sx ∧ ¬Px) ∀x (Sx → ¬Px) ¬∃x (Sx ∧ Px) ∀x (¬Sx ∨ Px)

56 If "Whenever X then Y" and "Y is true", what can be concluded about X?

X must be true X must be false X may be true or false Y causes X

57 Which is the contrapositive of "Only if P then Q"?

Only if Q then P If not Q then not P If Q then P Only if not P then not Q

58 In a valid syllogism, if a term is distributed in the conclusion:

It must be distributed in the premise It cannot be distributed in the premise The premise must be particular The conclusion must be negative

59 If "All A are B" and "Some C are not B", then:

Some C are not A No C are A All C are A No valid conclusion

60 Which correctly analyzes "All P are M. Some S are M. Therefore, some S are P"?

Valid Invalid - undistributed middle Invalid - illicit minor Invalid - existential fallacy

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Chapter 7: Logical Reasoning - Deduction