adminChapter 5: Syllogism – Understanding the Logic of Deductive Reasoning – 20 Questions
1. Who is credited with developing the notion of syllogism?
A. Plato
B. Socrates
C. Aristotle
D. Descartes
Answer: C
2. A syllogism consists of how many parts?
A. Two
B. Three
C. Four
D. Five
Answer: B
3. Which of the following is NOT a component of a syllogism?
A. Major premise
B. Minor premise
C. Conclusion
D. Counterexample
Answer: D
4. In Aristotle’s famous syllogism “All men are mortal; Socrates is a man; therefore, Socrates is mortal,” the major term is:
A. Socrates
B. Man
C. Mortal
D. Therefore
Answer: C
5. The minor premise in a syllogism provides:
A. A universal statement
B. A specific statement about an instance of the class
C. The final inference
D. An irrelevant distraction
Answer: B
6. The form “All A are B; All B are C; therefore, all A are C” is known as:
A. Ferio
B. Darii
C. Barbara
D. Clearent
Answer: C
7. Which syllogistic form is represented as “No A are B; All B are C; therefore, no A are C”?
A. Barbara
B. Clearent
C. Darii
D. Ferio
Answer: B
8. The conditional syllogism follows the form:
A. Either A or B; not A; therefore B
B. If A then B; if B then C; therefore, if A then C
C. All A are B; some A are C; therefore some B are C
D. No A are B; some A are C; therefore some C are not B
Answer: B
9. The disjunctive syllogism follows the form:
A. If A then B; A; therefore B
B. If A then B; not B; therefore not A
C. Either A or B; not A; therefore B
D. All A are B; not B; therefore not A
Answer: C
10. A valid syllogism is one where:
A. All premises are true
B. The conclusion follows necessarily from the premises
C. The conclusion is probable
D. The premises are popular
Answer: B
11. A sound syllogism requires:
A. Valid structure only
B. True premises only
C. Valid structure and true premises
D. Popular conclusion
Answer: C
12. “All cats lay eggs; Fluffy is a cat; therefore, Fluffy lays eggs” is an example of a(n):
A. Valid syllogism
B. Sound syllogism
C. Invalid syllogism
D. Conditional syllogism
Answer: C
13. In categorical syllogism, the middle term is:
A. The predicate of the conclusion
B. The subject of the conclusion
C. The term that appears in both premises but not in the conclusion
D. The term that appears only in the conclusion
Answer: C
14. The four valid syllogistic forms identified by Aristotle include all EXCEPT:
A. Barbara
B. Darii
C. Ferio
D. Brutus
Answer: D
15. “Some cats are black” is an example of which type of categorical proposition?
A. Universal affirmative (A)
B. Universal negative (E)
C. Particular affirmative (I)
D. Particular negative (O)
Answer: C
16. “No birds can swim” is an example of which type of categorical proposition?
A. A
B. E
C. I
D. O
Answer: B
17. The validity of a categorical syllogism depends on:
A. The truth of the content
B. The logical form only
C. The popularity of the premises
D. The length of the argument
Answer: B
18. Syllogism is most effective when dealing with:
A. Vague statements
B. Emotional appeals
C. Categorical statements that can be classified
D. Personal opinions
Answer: C
19. One limitation of syllogism is:
A. It is always sound
B. It cannot handle conditional statements
C. It is too flexible
D. It is only used in poetry
Answer: B
20. The contemporary application of syllogism includes all EXCEPT:
A. Law
B. Mathematics
C. Astrology
D. Critical thinking
Answer: C
Chapter 6: Basic Issues in Logic – Argument, Kinds of Arguments, and Laws of Thought – 20 Questions
1. Etymologically, the word “logic” is derived from the Greek word “logos” which means:
A. Law
B. Word, reason, study, or discourse
C. Number
D. Being
Answer: B
2. According to Copi (1998), logic is the study of:
A. The nature of reality
B. The methods and principles of differentiating correct from incorrect reasoning
C. The origin of language
D. The laws of nature
Answer: B
3. The three levels of logical process are:
A. Simple apprehension, judgment, reasoning/argument
B. Premise, conclusion, fallacy
C. Induction, deduction, syllogism
D. Observation, hypothesis, testing
Answer: A
4. Simple apprehension is:
A. The act of affirming or denying something
B. The act of forming a neutral concept without affirming or denying anything about it
C. The act of drawing a conclusion
D. The act of evaluating an argument
Answer: B
5. “Look at that bus” is an example of:
A. Judgment
B. Simple apprehension
C. Deductive argument
D. Inductive argument
Answer: B
6. Judgment in logic refers to:
A. The act of forming a neutral concept
B. The act by which the mind affirms or denies something of something else
C. The conclusion of a syllogism
D. A fallacy of ambiguity
Answer: B
7. In logic, the words “judgment,” “statement,” and “proposition” are generally:
A. Contradictory
B. Unrelated
C. Used interchangeably
D. Opposite in meaning
Answer: C
8. “All UNN students now take Computer Based Examination” is an example of:
A. Universal negative proposition
B. Particular affirmative proposition
C. Universal affirmative proposition
D. Particular negative proposition
Answer: C
9. “Some Nigerians are not hungry” is an example of:
A. Universal affirmative
B. Universal negative
C. Particular affirmative
D. Particular negative
Answer: D
10. A deductive argument moves from:
A. Particular to universal
B. Universal to particular
C. Conclusion to premises
D. Probability to certainty
Answer: B
11. The conclusion of a deductive argument is:
A. Probable
B. Necessarily certain if premises are true
C. Always false
D. Based on emotion
Answer: B
12. Inductive reasoning was founded by:
A. Aristotle
B. Plato
C. Francis Bacon
D. Descartes
Answer: C
13. The conclusion of an inductive argument is:
A. Necessarily true
B. Certain
C. Probable
D. Impossible
Answer: C
14. Which method is most used in scientific experimentation?
A. Deductive reasoning
B. Inductive reasoning
C. Syllogistic reasoning only
D. Fallacious reasoning
Answer: B
15. The law of identity states that:
A. A thing cannot be A and not A at the same time
B. If A then A; what is, is
C. There is no middle ground between truth and falsehood
D. Everything changes
Answer: B
16. The law of contradiction (non-contradiction) states that:
A. What is, is
B. Something cannot be A and not A at the same time
C. Either A or not A, no middle
D. All things change
Answer: B
17. The law of excluded middle states that:
A. A thing is identical to itself
B. Nothing can be both A and not A
C. Either a proposition is true or its negation is true; there is no middle
D. All reasoning is probabilistic
Answer: C
18. According to Aja (2008), the laws of thought:
A. Can be easily disproved
B. Cannot be proved beyond them nor disproved beyond necessity
C. Are irrelevant to logic
D. Apply only to deductive arguments
Answer: B
19. “All thinking is reasoning but not all reasoning is thinking” implies that:
A. Thinking and reasoning are identical
B. Reasoning is a methodical form of thinking
C. Reasoning is random
D. Thinking is always logical
Answer: B
20. In deductive argument, the premises provide:
A. Probable support for the conclusion
B. All the reasons for the conclusion
C. Emotional appeal
D. Irrelevant information
Answer: B
Chapter 7: Logical Fallacies and Their Applications – 20 Questions
1. A fallacy is:
A. A valid argument
B. A deceptively bad argument that appears correct
C. A sound syllogism
D. A type of proposition
Answer: B
2. Fallacies are deceptive because they:
A. Are always false
B. Appear correct on the surface but are not
C. Have no premises
D. Are never used in real life
Answer: B
3. Appeal to pity is also known as:
A. Argumentum ad populum
B. Argumentum ad misericordiam
C. Argumentum ad hominem
D. Argumentum ad verecundiam
Answer: B
4. The fallacy of appealing to popular beliefs or desires is called:
A. Appeal to pity
B. Appeal to people (argumentum ad populum)
C. Straw man
D. Red herring
Answer: B
5. The bandwagon argument is a form of:
A. Appeal to pity
B. Appeal to people (indirect)
C. Straw man
D. Complex question
Answer: B
6. Adolf Hitler is noted in the text as a master of which fallacy?
A. Appeal to pity
B. Appeal to people (direct)
C. Straw man
D. False dichotomy
Answer: B
7. The straw man fallacy involves:
A. Appealing to pity
B. Misrepresenting an opponent’s position to make it easier to attack
C. Using a complex question
D. Begging the question
Answer: B
8. The red herring fallacy uses:
A. Emotional appeal
B. Distraction to divert attention from the original issue
C. Circular reasoning
D. Ambiguous terms
Answer: B
9. The term “red herring” originated from:
A. A type of fish used to train hunting dogs
B. A political speech
C. A mathematical proof
D. A legal document
Answer: A
10. Ignoratio elenchi means:
A. Appeal to ignorance
B. Missing the point or ignorance of refutation
C. Begging the question
D. False dichotomy
Answer: B
11. Fallacies of weak induction occur when:
A. The premises are irrelevant
B. The premises are relevant but not adequate to support the conclusion
C. The argument is valid
D. The conclusion is certain
Answer: B
12. “Have you stopped stealing?” is an example of which fallacy?
A. Begging the question
B. Complex question
C. False dichotomy
D. Equivocation
Answer: B
13. Begging the question is also known as:
A. Circular argument
B. Red herring
C. Straw man
D. Appeal to pity
Answer: A
14. The fallacy of equivocation occurs when:
A. A word is used in two different meanings in an argument
B. A question is asked in a misleading way
C. An appeal is made to popular belief
D. The conclusion is assumed in the premise
Answer: A
15. “We have a bright light; the cup is light; therefore, the cup is bright” commits which fallacy?
A. Amphiboly
B. Equivocation
C. Composition
D. Division
Answer: B
16. The fallacy of amphiboly arises from:
A. Ambiguous word meaning
B. Ambiguous grammar or punctuation
C. False premise
D. Irrelevant conclusion
Answer: B
17. The fallacy of composition is committed when one:
A. Argues that what is true of the whole is true of the parts
B. Argues that what is true of the parts is true of the whole
C. Uses a complex question
D. Appeals to pity
Answer: B
18. The fallacy of division is the opposite of:
A. Equivocation
B. Amphiboly
C. Composition
D. Begging the question
Answer: C
19. “The University of Nigeria is an important institution; Dr. Okeke is a lecturer there; therefore, Dr. Okeke is important” commits which fallacy?
A. Composition
B. Division
C. Equivocation
D. Straw man
Answer: B
20. False dichotomy is also known as:
A. Either-or fallacy
B. Begging the question
C. Red herring
D. Complex question
Answer: A
Chapter 8: Basic Symbolic Logic and Computational Technology – 20 Questions
1. Symbolic logic is also called:
A. Informal logic
B. Formal logic
C. Natural logic
D. Emotional logic
Answer: B
2. Which of the following is NOT a focus of formal logic?
A. Strict rules
B. Symbols for evaluation
C. Real-life context of reasoning
D. Abstract representation
Answer: C
3. In symbolic logic, simple statements are represented by:
A. Numbers
B. Lower case alphabets (p, q, r)
C. Greek letters
D. Arrows only
Answer: B
4. The logical connective for “and” is often symbolized as:
A. V
B. →
C. . (dot)
D. ~
Answer: C
5. The symbol “~” (curl/tilde) represents:
A. And
B. Or
C. Not
D. If…then
Answer: C
6. The symbol “V” (vel/wedge) represents:
A. And
B. Or (inclusive)
C. Not
D. If and only if
Answer: B
7. A truth-table shows:
A. The emotional value of statements
B. The truth-value of compound statements for all possible truth-values of components
C. The popularity of an argument
D. The length of an argument
Answer: B
8. In a truth-table for conjunction (p.q), the compound statement is true only when:
A. Both p and q are true
B. At least one is true
C. Both are false
D. One is true and one false
Answer: A
9. In a truth-table for inclusive disjunction (p v q), the compound statement is false only when:
A. Both are true
B. Both are false
C. One is true, one false
D. At least one is true
Answer: B
10. The branch of symbolic logic that deals with possibility and necessity is:
A. Fuzzy logic
B. Temporal logic
C. Modal logic
D. Predicate logic
Answer: C
11. Deontic modality deals with:
A. Necessity and possibility
B. Knowledge and belief
C. Obligation and permission
D. Time sequences
Answer: C
12. Fuzzy logic represents truth as:
A. Only true or false
B. Degrees of truth between 0 and 1
C. Always false
D. Always true
Answer: B
13. Temporal logic expresses:
A. Possibility and necessity
B. Time-dependent statements
C. Obligations
D. Degrees of truth
Answer: B
14. Which thinker is NOT mentioned as favouring symbolic logic?
A. Gottfried Wilhelm Leibniz
B. George Boole
C. Bertrand Russell
D. John Locke
Answer: D
15. In programming, the symbol “&&” represents:
A. Logical OR
B. Logical AND
C. Logical NOT
D. Logical equality
Answer: B
16. In Boolean logic, “!” typically represents:
A. And
B. Or
C. Negation (NOT)
D. Implication
Answer: C
17. The binary system (0 & 1) in computing is an application of:
A. Fuzzy logic
B. Two-valued logic
C. Temporal logic
D. Modal logic
Answer: B
18. Which branch of logic is useful in control systems like autonomous vehicles?
A. Fuzzy logic
B. Modal logic
C. Temporal logic
D. Predicate logic
Answer: A
19. According to the text, symbolic logic was developed to:
A. Replace natural language entirely
B. Imitate human reasoning with precision and avoid ambiguity
C. Make reasoning emotional
D. Eliminate mathematics
Answer: B
20. E-commerce platforms use symbolic logic to:
A. Create poetry
B. Personalize advertisements and drive sales
C. Replace human workers
D. Eliminate data
Answer: B
SUMMARIES
Chapter 5: Syllogism – Understanding the Logic of Deductive Reasoning
This chapter focuses on syllogism, a deductive reasoning tool developed by Aristotle. A syllogism consists of three parts: major premise, minor premise, and conclusion. It uses categorical propositions (A, E, I, O). The four valid syllogistic forms are Barbara, Clearent, Darii, and Ferio. The chapter also explains conditional syllogism (if-then chains) and disjunctive syllogism (either-or, therefore). Key distinctions: validity (logical structure) vs. soundness (valid + true premises). Applications include law, mathematics, computer science, and critical thinking. Limitations include difficulty with vague or probabilistic statements.
Chapter 6: Basic Issues in Logic – Argument, Kinds of Arguments, and Laws of Thought
Logic is defined as the science of correct reasoning (Copi). The three levels of logical process are: simple apprehension (neutral concept formation), judgment (affirmation/denial), and reasoning/argument. Propositions are classified into four types: universal affirmative (A), universal negative (E), particular affirmative (I), particular negative (O). Arguments are divided into deductive (universal → particular; conclusion certain) and inductive (particular → universal; conclusion probable). Deduction originates with Aristotle; induction with Francis Bacon. The three laws of thought (Aristotle) are: Identity (what is, is), Non-contradiction (cannot be A and not A), and Excluded Middle (no middle between true and false).
Chapter 7: Logical Fallacies and Their Applications
A fallacy is a deceptively bad argument that appears correct. Fallacies are classified into:
- Fallacies of relevance (premises irrelevant): appeal to people (ad populum), appeal to pity (ad misericordiam), straw man, red herring, missing the point (ignoratio elenchi).
- Fallacies of weak induction (premises relevant but insufficient): hasty generalization, false cause, weak analogy.
- Fallacies of presumption (hidden assumptions): false dichotomy (either-or), complex question (plurium interrogationum), begging the question (petitio principii – circular argument).
- Fallacies of ambiguity: equivocation (same word, different meanings), amphiboly (grammatical ambiguity).
- Fallacies of grammatical analogy: composition (part → whole) and division (whole → part).
The ability to detect fallacies is essential for critical thinking.
Chapter 8: Basic Symbolic Logic and Computational Technology
Symbolic logic (formal logic) uses artificial symbols to represent statements, avoiding ambiguities of natural language. Simple statements are represented by letters (p, q, r). Logical connectives include: dot (•) for and, tilde (~) for not, wedge (∨) for or, horseshoe (⊃) for if…then, and double arrow (≡) for if and only if. Truth-tables determine truth-values of compound statements. Branches discussed: modal logic (necessity/possibility, obligation, time), fuzzy logic (degrees of truth 0–1), temporal logic (time-dependent statements). The chapter links symbolic logic to computational technology: programming languages (Python, Java, C++), Boolean operators (&&, ||, !), binary code (0/1), and applications in AI, e-commerce, and control systems. Symbolic logic enables precision, consistency, and scalability in computing.
KEY NOTES
Chapter 5 – Syllogism
- Syllogism = deductive argument with two premises and a conclusion (developed by Aristotle).
- Three components: major premise, minor premise, conclusion.
- Categorical propositions: A (All S is P), E (No S is P), I (Some S is P), O (Some S is not P).
- Four valid syllogistic forms (Aristotle):
- Barbara – All A are B; All B are C; ∴ All A are C.
- Clearent – No A are B; All B are C; ∴ No A are C.
- Darii – Some A are B; All B are C; ∴ Some A are C.
- Ferio – Some A are not B; All B are C; ∴ Some A are not C.
- Three terms in categorical syllogism: major term, minor term, middle term.
- Conditional syllogism (hypothetical): If A then B; If B then C; ∴ If A then C.
- Disjunctive syllogism: Either A or B; Not A; ∴ B.
- Validity = conclusion follows necessarily from premises (structure).
- Soundness = valid + all premises true.
- Limitations: works best with clear categories; less effective with vague or probabilistic statements.
Chapter 6 – Basic Issues in Logic (Argument, Kinds of Arguments, Laws of Thought)
- Logic (etymology: logos = word, reason, study) = science of correct reasoning (Copi).
- Three levels of logical process:
- Simple apprehension – neutral concept formation (no affirmation/denial). Example: “Look at that bus.”
- Judgment – affirming or denying something of something else. Example: “My VC is tall.”
- Reasoning/argument – drawing conclusions from premises.
- Four types of propositions:
- Universal Affirmative (A) – All S are P.
- Universal Negative (E) – No S are P.
- Particular Affirmative (I) – Some S are P.
- Particular Negative (O) – Some S are not P.
- Deductive argument (Aristotle): universal → particular; conclusion certain if premises true.
- Inductive argument (Francis Bacon): particular → universal; conclusion probable (used in science).
- Three Laws of Thought (Aristotle):
- Identity – What is, is (A = A).
- Non-contradiction – Cannot be A and not A at the same time.
- Excluded Middle – Either A or not A; no middle ground.
Chapter 7 – Logical Fallacies
- Fallacy = deceptively bad argument that appears correct.
- Fallacies of relevance (premises irrelevant):
- Appeal to people (ad populum) – uses popular beliefs/desires. Forms: bandwagon, appeal to vanity, appeal to snobbery.
- Appeal to pity (ad misericordiam) – uses emotion/mercy.
- Straw man – misrepresents opponent’s position to attack it easily.
- Red herring – distracts by changing the topic.
- Missing the point (ignoratio elenchi) – conclusion different from what premises support.
- Fallacies of weak induction (premises relevant but insufficient): hasty generalization, false cause, weak analogy.
- Fallacies of presumption (hidden assumptions):
- False dichotomy (either-or fallacy) – presents only two options when more exist.
- Complex question (plurium interrogationum) – asks a question that presupposes a hidden conclusion. Example: “Have you stopped stealing?”
- Begging the question (petitio principii – circular argument) – conclusion assumed in premises.
- Fallacies of ambiguity:
- Equivocation – same word used with different meanings in argument.
- Amphiboly – ambiguous grammar/punctuation leads to wrong conclusion.
- Fallacies of grammatical analogy:
- Composition – what is true of the parts is true of the whole.
- Division – what is true of the whole is true of the parts.
Chapter 8 – Basic Symbolic Logic and Computational Technology
- Symbolic logic (formal logic) = uses artificial symbols to represent statements, avoiding ambiguity.
- Statement variables: lower case letters (p, q, r).
- Logical connectives (truth-functional operators):
| Word | Symbol | Name |
|---|---|---|
| and | • (dot) | Conjunction |
| not | ~ (tilde) | Negation |
| or (inclusive) | ∨ (wedge) | Disjunction |
| if…then | ⊃ (horseshoe) | Implication |
| if and only if | ≡ (double arrow) | Equivalence |
- Truth-table – shows truth-value of compound statement for all possible truth-values of components.
- Conjunction (p•q): True only when both true.
- Disjunction (p∨q): False only when both false.
- Branches of symbolic logic:
- Modal logic – necessity/possibility, obligation/permission (deontic), knowledge (epistemic), time (temporal).
- Fuzzy logic – degrees of truth between 0 and 1 (not just true/false).
- Temporal logic – time-dependent statements (always, sometimes, next).
- Link to computational technology:
- Programming languages use logical operators: && (AND), || (OR), ! (NOT).
- Binary code (0 & 1) = two-valued logic.
- Applications: AI, e-commerce, control systems, machine learning.
- Key thinkers who favoured symbolic logic: Leibniz, Boole, De Morgan, Frege, Russell, Tarski, Gödel.
Quick Revision – Names to Remember (Section Two)
| Name | Key Idea |
|---|---|
| Aristotle | Syllogism; laws of thought; four valid forms (Barbara, Clearent, Darii, Ferio); deduction |
| Francis Bacon | Inductive reasoning |
| Copi | Logic = science of correct reasoning |
| Hurley | Fallacies classification |
| Leibniz, Boole, Frege, Russell | Developed symbolic logic |
