Tiêu đề MCQ DISCRETE MATHEMATICS.pdf ✅

Way to Polytechnic ● Way to Polytechnic DISCRETE MATHEMATICS Unit – 1 The Foundations- Logic and Proofs 1. What is the basic building block in propositional logic? a) Predicate b) Proposition c) Quantifier d) Inference 2. Which of the following represents a logical connective in propositional logic? a) + b) ^ c) / d) * 3. Which of the following is NOT a propositional equivalence? a) Double Negation Law b) Commutative Law c) Distributive Law d) Associative Law 4. In logic, what is a predicate? a) A statement that is either true or false b) A symbol that represents a logical connective c) A function that maps propositions to truth values d) A variable that represents an unknown value 5. What is the purpose of quantifiers in predicate logic? a) To connect predicates b) To represent logical connectives c) To specify the scope of variables d) To perform proof by contradiction 6. What does the symbol "∀" represent in predicate logic? a) There exists b) For all c) Implies 1
Way to Polytechnic ● Way to Polytechnic d) Logical AND 7. In nested quantifiers, how is the order of quantifiers determined? a) Randomly b) Alphabetically c) By the order of appearance d) According to a predefined rule 8. Which of the following is a valid rule of inference? a) Transitive Property b) Distributive Law c) Contrapositive d) Inverse 9. What is the main purpose of a proof in mathematics? a) To demonstrate a statement's truth b) To confuse readers c) To introduce new concepts d) To provide examples 10. What is the goal of the proof by contradiction method? a) To prove a statement directly b) To assume the negation and derive a contradiction c) To simplify complex expressions d) To establish logical equivalences 11. Which of the following is a normal form in propositional logic? a) Conjunctive Normal Form (CNF) b) Disjunctive Normal Form (DNF) c) Conjunctive Equivalence Form (CEF) d) Disjunctive Equivalence Form (DEF) 12. What does the De Morgan's Law state in propositional logic? a) ¬(P ∧ Q) ≡ ¬P ∧ Q b) ¬(P ∨ Q) ≡ ¬P ∨ Q c) ¬(P → Q) ≡ ¬P → Q d) ¬(P ↔ Q) ≡ ¬P ↔ Q 2
Way to Polytechnic ● Way to Polytechnic 13. In a direct proof, how is the conclusion reached? a) By contradiction b) By assuming the negation c) By induction d) By establishing a chain of logical reasoning 14. What does the proof by contrapositive method involve? a) Proving the converse of the statement b) Proving the negation of the contrapositive c) Proving the negation of the original statement d) Proving the contrapositive directly 15. In proof strategy, what does "divide and conquer" refer to? a) Breaking down a complex problem into simpler subproblems b) Creating a divide between true and false statements c) Using the division property in inequalities d) Dividing the proof into separate sections 16. What is the purpose of modus ponens in inference rules? a) To simplify logical expressions b) To derive a conclusion from a conditional statement and its antecedent c) To introduce new variables d) To establish equivalence relations 17. Which of the following is an example of an existential quantifier? a) ∃ b) ∀ c) ⇒ d) ↔ 18. What is the role of universal quantifiers in mathematical statements? a) To indicate the existence of a unique solution b) To specify a property that holds for all elements in a set c) To represent conditional statements d) To establish a contradiction 19. What is a tautology in propositional logic? a) A statement that is always true b) A statement that is always false 3
Way to Polytechnic ● Way to Polytechnic c) A statement that is sometimes true d) A statement that involves quantifiers 20. Which of the following is a valid proof technique? a) Wishful thinking b) Proof by intimidation c) Proof by example d) Proof by contradiction Answers: 1. b) Proposition 2. b) ^ 3. d) Associative Law 4. c) A function that maps propositions to truth values 5. c) To specify the scope of variables 6. b) For all 7. c) By the order of appearance 8. c) Contrapositive 9. a) To demonstrate a statement's truth 10. b) To assume the negation and derive a contradiction 11. a) Conjunctive Normal Form (CNF) 12. b) ¬(P ∨ Q) ≡ ¬P ∨ Q 13. d) By establishing a chain of logical reasoning 14. c) Proving the negation of the original statement 15. a) Breaking down a complex problem into simpler subproblems 16. b) To derive a conclusion from a conditional statement and its antecedent 17. a) ∃ 18. b) To specify a property that holds for all elements in a set 19. a) A statement that is always true 20. c) Proof by example 4