Logical Reasoning Fundamentals

Q1. A=true, B=true. A AND B?

1. A.True✓ Correct
2. B.False
3. C.Null
4. D.Undefined

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Q2. NOT True?

1. A.Error
2. B.True
3. C.False✓ Correct
4. D.Null

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Q3. A=true, B=false. A OR B?

1. A.True✓ Correct
2. B.Neither
3. C.Undefined
4. D.False

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Q4. General to specific reasoning?

1. A.Abductive
2. B.Inductive
3. C.Analogical
4. D.Deductive✓ Correct

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Q5. Specific to general reasoning?

1. A.Deductive
2. B.Abductive
3. C.Inductive✓ Correct
4. D.Circular

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Q6. Truth table with 2 variables has how many rows?

1. A.16
2. B.4✓ Correct
3. C.2
4. D.8

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Q7. What is a logical fallacy?

1. A.A correct logical argument
2. B.An error making argument invalid✓ Correct
3. C.A type of search algorithm
4. D.A specific data structure

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Q8. All cats are animals. Tom is a cat. Therefore?

1. A.Tom is actually a dog
2. B.Nothing can be concluded
3. C.Tom is not an animal
4. D.Tom is an animal too✓ Correct

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Q9. What does XOR return?

1. A.Always returns true as output
2. B.True when exactly one is true✓ Correct
3. C.Always returns false as output
4. D.True when both inputs are true

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Q10. What is a premise?

1. A.A conclusion drawn from evidence
2. B.A statement assumed true for reasoning✓ Correct
3. C.A question posed to the audience
4. D.An error found in the argument

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Q11. Contrapositive of If P then Q?

1. A.If P then not Q
2. B.If not Q then not P✓ Correct
3. C.If Q then P
4. D.If not P then not Q

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Q12. Which is De Morgan's Law?

1. A.NOT A = A
2. B.NOT(A AND B) = NOT A OR NOT B✓ Correct
3. C.A AND B = A OR B
4. D.A XOR B = A AND B

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Q13. What is modus ponens?

1. A.P->Q, P false, therefore Q false
2. B.P->Q, Q false, therefore P false
3. C.P->Q, Q true, therefore P
4. D.P->Q, P true, therefore Q✓ Correct

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Q14. What is modus tollens?

1. A.P->Q, P true, therefore Q
2. B.P->Q, Q true, therefore P
3. C.P->Q, Q false, therefore P false✓ Correct
4. D.P->Q, P false, therefore Q false

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Q15. Truth table with 4 variables?

1. A.16 rows✓ Correct
2. B.32 rows
3. C.8 rows
4. D.4 rows

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Q16. What is a tautology?

1. A.Always true regardless of values✓ Correct
2. B.A logical contradiction in reasoning
3. C.A statement that is always false
4. D.A statement that is sometimes true

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Q17. What is a contradiction?

1. A.Always false regardless of values✓ Correct
2. B.A tautology under all conditions
3. C.A valid argument with true premises
4. D.A statement that is always true

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Q18. What does P <-> Q mean?

1. A.P implies Q in one direction only
2. B.P is true if and only if Q is true✓ Correct
3. C.Q implies P in one direction only
4. D.Both P and Q are always true together

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Q19. What is proof by contradiction?

1. A.A type of mathematical induction
2. B.Proving the statement is false
3. C.A direct proof from axioms
4. D.Assume opposite, show contradiction✓ Correct

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Q20. Affirming the consequent fallacy?

1. A.Rain->wet. No rain. Not wet.
2. B.Rain->wet. Dry. No rain.
3. C.Rain->wet. Wet. Therefore rained.✓ Correct
4. D.Rain->wet. Rained. Wet.

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Q21. Universal quantifier means?

1. A.For exactly one element only
2. B.For all elements in the domain✓ Correct
3. C.For no elements in the domain
4. D.There exists at least one element

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Q22. Negation of forall x P(x)?

1. A.exists x NOT P(x)✓ Correct
2. B.forall x NOT P(x)
3. C.NOT exists x P(x)
4. D.forall x P(x) still

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Q23. What is mathematical induction?

1. A.Proving base case plus if n then n+1✓ Correct
2. B.Testing all possible cases manually
3. C.Guessing the answer to the problem
4. D.Only proving the base case alone

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Q24. What is a clause in resolution?

1. A.A disjunction of logical literals✓ Correct
2. B.A conjunction of several functions
3. C.A complete executable program
4. D.A variable assignment statement

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Q25. Logical completeness means?

1. A.The system runs very fast
2. B.The system has no bugs at all
3. C.Every valid formula is provable✓ Correct
4. D.It uses all logical operators

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Q26. Godel's first incompleteness theorem?

1. A.All formal systems are complete
2. B.All true statements are provable
3. C.Consistent systems have unprovable truths✓ Correct
4. D.Logic is unnecessary for proofs

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Q27. What is satisfiability (SAT)?

1. A.Whether an assignment makes it true✓ Correct
2. B.A formula that is always true
3. C.A formula with no variable bindings
4. D.A formula that is always false

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Q28. What is soundness?

1. A.It uses auditory signal processing
2. B.The system proves everything possible
3. C.The system has zero error states
4. D.Every provable statement is valid✓ Correct

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Q29. SAT worst case?

1. A.O(n^2) quadratic time
2. B.O(n) linear time
3. C.Exponential (NP-complete)✓ Correct
4. D.O(n log n) linearithmic

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Q30. What is semantic entailment?

1. A.A programming concept for objects
2. B.A specific data type for storage
3. C.A syntax rule in formal languages
4. D.Premises true implies conclusion true✓ Correct

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