Logic & Formal Reasoning

أسئلة الاختبار

1. 1. Identify the conclusion of the following argument. It is hard not to verify in our peers the same weakened intelligence due to emotions that we observe in our everyday patients. The arrogance of our consciousness, which in general, belongs to the strongest defense mechanisms, blocks the unconscious complexes. Because of this, it is difficult to convince people of the unconscious, and in turn to teach them what their conscious knowledge contradicts. (Sigmund Freud, The Origin and Development of Psychoanalysis)
   1. It is hard not to verify in our peers the same weakened intelligence due to emotions that we observe in our everyday patients.
   2. The arrogance of our consciousness, which in general, belongs to the strongest defense mechanisms, blocks the unconscious complexes.
   3. Because of this, it is difficult to convince people of the unconscious, and in turn to teach them what their conscious knowledge contradicts.
   4. It is difficult to convince people of the unconscious, and in turn to teach them what their conscious knowledge contradicts.
2. 2. Select the best translation into predicate logic. David teaches Chris. (c: Chris; d: David; Txy: x teaches y)
   1. Tdc
   2. Tcd
   3. Tcc
   4. dTc
3. 3. Select the best English interpretation of the given proposition, using the following translation key: Ax: x is an apartment Hx: x is a house Lx: x is large Bxy: x is bigger than y (∃x)[(Ax • Lx) • (∃y)(Hy • Bxy)]
   1. Some large houses are bigger than some apartments.
   2. Some houses are bigger than all large apartments.
   3. Some large apartments are bigger than some houses.
   4. Some houses are bigger thatn some large apartments.
4. 4. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
   ~G ⊃ H
   ~H / G
   1. Valid
   2. Invalid. Counterexample when G and H are true
   3. Invalid. Counterexample when G is true and H is false
   4. Invalid. Counterexample when H is true and G is false
5. 5. Use the following key to translate the given formula of PL to natural, English sentences.
   A: Marina reads a Percy Jackson book.
   B: Izzy plays Minecraft.
   C: Emily stops working.
   D: Russell makes dinner.
   E: Ashleigh stops by.
   (~B • E) ⊃ D
   1. If it's not the case that both Izzy plays Minecraft and Ashleigh stops by then Russell makes dinner.
   2. If it's both not the case that Izzy plays Minecraft and Ashleigh stops by then Russell makes dinner.
   3. Izzy playing Minecraft and Ashleigh stopping by entails that Russell makes dinner.
   4. Russell's making dinner is a sufficient condition for Izzy not playing Minecraft and Ashleigh stopping by.
6. 6. Select the best English interpretation of the given proposition, using the following translation key: Ax: x is an apartment Hx: x is a house Lx: x is large Bxy: x is bigger than y (∃x)[Hx • (∀y)(Ay ⊃ Bxy)]
   1. Some houses are smaller than all apartments.
   2. Every house is bigger than every apartment.
   3. Some apartment is smaller than every house.
   4. Some houses are bigger than every apartment.
7. 7. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
   ~K ≡ L / (K · L) ∨ (K · ~L)
   1. Valid
   2. Invalid. Counterexample when K and L are true
   3. Invalid. Counterexample when K is true and L is false
   4. Invalid. Counterexample when L is true and K is false
8. 8. Identify the antecedent of the following conditional proposition: If the university does not increase financial aid, either the president fails to approve it or the board of trustees prevents it.
   1. The university increases financial aid.
   2. The university does not increase financial aid.
   3. The board of trustees prevents it.
   4. The president fails to approve it.
9. 9. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?
   ~E ⊃ ~F
   G ⊃ F
   H ∨ ~E
   H ⊃ I
   ~I
   1. E ⊃ F
   2. F ⊃ G
   3. H ⊃ ~E
   4. ~H
10. 10. Which of the given formulas of PL is the best symbolization of the following sentence?
    Everybody loves Raymond, or not.
    1. L
    2. ~L
    3. L • ~L
    4. L ∨ ~L
11. 11. Select the best translation into predicate logic. All kings are luckier than all paupers. (Kx: x is a king; Px: x is a pauper; Lxy: x is luckier than y)
    1. (∀x)[Kx ⊃ (∀y)(Py ⊃ Lxy)]
    2. (∀x)[Kx ⊃ (∀y)(Lxy ⊃ Py)]
    3. (∀x)(∀y)[(Kx • Py) ⊃ Lyx]
    4. (∀x)[(Kx • (∀y)(Py)) ⊃ Lxy]
12. 12. Construct a complete truth table for the following pairs of propositions. Then, using the truth tables, determine whether the statements are logically equivalent or contradictory. If neither, determine whether they are consistent or inconsistent. Justify your answers.
    (~M ⊃ ~N) ∨ (O ≡ N) and (~M · N) · [(~O ∨ ~N) · (O ∨ N)]
    1. Logically equivalent
    2. Contradictory
    3. Neither logically equivalent nor contradictory, but consistent
    4. Inconsistent
13. 13. Which of the following propositions is an immediate (one-step) consequence in PL of the given premises?
    E ⊃ ~F
    ~F ⊃ G
    ~G
    1. E ⊃ F
    2. F ⊃ G
    3. G ⊃ E
    4. ~~F
14. 14. Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
    E ⊃ (F ∨ ~G)
    F ⊃ (~E ∨ ~G) / ~(E ≡ F)
    1. Valid
    2. Invalid. Counterexample when E, F, and G are true
    3. Invalid. Counterexample when E and F are true and G is false
    4. Invalid. Counterexample when E, F, and G are false
15. 15. Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
    H ≡ (~I ∨ J)
    H ∨ ~J / ~I
    1. Valid
    2. Invalid. Counterexample when H, I, and J are false
    3. Invalid. Counterexample when H and I are true and J is false
    4. Invalid. Counterexample when I is true and H and J are false
16. 16. Select the best translation into predicate logic. Some firefighters rescue victims from danger. (Dx: x is danger; Fx: x is a firefighter; Vx: x is a victim; Rxyz: x rescues y from z)
    1. (∃x){Fx • (∀y)[Dy ⊃ (∃z)(Vz • Rxyz)]}
    2. (∃x){Fx • (∃y)[Vy • (∃z)(Dz • Rxyz)]}
    3. (∃x){Fx • (∃y)(∃z)[(Vy • Dz) • Rxzy]}
    4. (∀x){Fx ⊃ (∃y)[Vy . (∃z)(Dz • Rxyz)]}
17. 17. Identify the antecedent of the following conditional proposition: The university raises tuition if, and only if, both the governor approves of it and the board of trustees recommends it.
    1. The university raises tuition.
    2. The governor approves of it.
    3. The board of trustees recommends it.
    4. None of the above
18. 18. A valid disjunctive syllogism has a major premise that:
    1. includes two or more alternatives
    2. classifies subjects
    3. affirms the antecedent or denies the consequent
    4. leads to a valid conclusion
19. 19. Which of the following best describes the fallacy of style over substance?
    1. Changing the meaning of a word or phrase from one part of the argument to another.
    2. Confusing figurative language with literal language.
    3. Reasoning that ideas presented in an appealing manner are correct, regardless of the content of the message.
    4. Using emotionally charged language to create an impression about the subject of a claim, without making an argument that the language fits the subject.
20. 20. Which of the following fallacies is a way of suppressing evidence that eliminates a source of evidence from consideration by claiming the source is flawed, when there is no true relationship between the alleged flaw and the reliability of the source?
    1. significance
    2. snob appeal
    3. poisoning the well
    4. appeal to anonymous authority
21. 21. The false analogy fallacy is
    1. a specific type of false cause fallacy that argues that since two event happened at the same time one event must have caused the other
    2. arguing that an event that preceded another event necessarily is the cause of the second event
    3. arguing that since something is new it is necessarily good
    4. drawing a conclusion based on a comparison when the items being compared are not similar enough to support the conclusion.
22. 22. The _ad nauseam_ fallacy is
    1. arguing that something should be done because that's the way it's been done in the past.
    2. arguing that an act should be carried out because it will not have any significant consequences, when there is no evidence of the effects
    3. reasoning that a conclusion is true because it's been claimed so often
    4. reasoning that a claim is true because so many people believe it is true
23. 23. Arguing that what is true of an entire object is also true of each part of that object is the fallacy of
    1. false criteria
    2. hasty generalization
    3. ad crumenam
    4. division
24. 24. Which of the following describes the horse laugh fallacy?
    1. responding to an argument with an expression of derision instead of a counter argument
    2. attempts to gain agreement based solely the feelings aroused by the message
    3. characterizing an opponent's position in such way to make it or its consequences appear to be ridiculous
    4. arguing actions should be taken to avoid negative results, when those results are exaggerated, unlikely, or irrelevant
25. 25. Arguing that a lack of evidence proves something is the fallacy of...
    1. Appeal to ignorance
    2. Double negative
    3. Equivocation
    4. Burden of proof
26. 26. The argument against the person consists of
    1. ignoring another person's arguments and attacking her character instead
    2. asserting an opposing arguer has taken an easily defeated position, which she has not really taken
    3. causing confusion during an argument by a lack of ability to engage in refutation
    4. using threats of harm instead of reasoning to gain agreement
27. 27. Which of the following fallacies happens when someone concludes that someone must be honest because the people he hangs around with are honest?
    1. Laudatory personality
    2. Guilt by association
    3. Reprehensible personality
    4. Circular reasoning
28. 28. Asking a question that includes an unproven assumption may lead to which of the following fallacies?
    1. Appeal to ignorance
    2. Extension
    3. a priori
    4. Complex question
29. 29. Polonius in William Shakespeare's Hamlet: "Your noble son is mad: Mad call I it, for to define true madness, What is't but to be nothing else but mad?"
    1. Attacking the Person (ad hominem)
    2. Equivocation
    3. Begging the Question
    4. Appeal to Pity
30. 30. Notice from the Hyatt Regency Hotel in New Orleans: We are pleased to confirm your reservation. It will be held on a space-available basis.
    1. Equivocation
    2. Affirming the Consequent
    3. Gambler's Fallacy
    4. Inconsistency