Podcast
Questions and Answers
Which of the following is a well-formed propositional formula?
Which of the following is a well-formed propositional formula?
- (p ∧ q) → (q ∨ r)
- ¬(p → (q ∧ p)) (correct)
- p → (q ∧ ¬p)
- p ∨ (q ∨ p¬r)
If p → q is false, what can be inferred about the truth values of p and q?
If p → q is false, what can be inferred about the truth values of p and q?
- p is true and q is false. (correct)
- Both p and q are true.
- Both p and q are false.
- p is false and q is true.
How would you formalize the statement: 'Only one among Amit, Bimal, and Chandra passed the exam'?
How would you formalize the statement: 'Only one among Amit, Bimal, and Chandra passed the exam'?
- A ∧ ¬B ∧ ¬C
- (A ∧ ¬B) ∨ (B ∧ ¬C) ∨ (C ∧ ¬A) (correct)
- A ∨ B ∨ C
- (A ∨ B) ∧ ¬(A ∧ B) ∧ ¬C
What is the required conclusion for the formal proof: (p ∧ (p → q) ∧ (s ∨ r) ∧ (r → ¬q)) → (s ∨ t)?
What is the required conclusion for the formal proof: (p ∧ (p → q) ∧ (s ∨ r) ∧ (r → ¬q)) → (s ∨ t)?
How can the proposition (p(0, 0) ∨ p(0, 1)) ∧ (p(1, 0) ∨ p(1, 1)) be represented by a quantified expression?
How can the proposition (p(0, 0) ∨ p(0, 1)) ∧ (p(1, 0) ∨ p(1, 1)) be represented by a quantified expression?
What free variable exists in the well-formed formula ∀x(p(x) → ∃y¬q(f(x), y, f(y)))?
What free variable exists in the well-formed formula ∀x(p(x) → ∃y¬q(f(x), y, f(y)))?
Which of the following expressions contains free variables?
Which of the following expressions contains free variables?
What does the well-formed formula ∀x∃y p(x, f(y)) → q(x, y) imply?
What does the well-formed formula ∀x∃y p(x, f(y)) → q(x, y) imply?
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Study Notes
Quiz Format and Submission Instructions
- Answers must be on blank sheets and in the order of the questions.
- Convert responses into a single PDF file for submission.
- File naming convention: RollNo-Q1.pdf (e.g., 200109009-Q1.pdf).
- Include name and roll number at the top of each page.
- Maximum of three pages allowed for answers.
- Collaboration is prohibited and will incur penalties.
Quiz Structure
- Total Questions: 8
- Maximum Marks: 40
- Time Limit: 40 Minutes
Propositional Logic Questions
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Well-formed Propositional Formulas:
- Identify which formulas among given options are correctly structured.
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Truth Value Evaluation:
- Analyze the truth value of the expression (¬p ∧ q) ↔ (p ∨ q) when p → q is false.
Propositions and Formalization
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Propositions for Students:
- Define propositions: A (Amit passed), B (Bimal passed), C (Chandra passed).
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Sentence Formalization:
- Formalize "only one passed" using logical notation.
- Formalize "exactly two passed" using propositional logic.
Formal Proof
- Required Proof:
- Prove the implication (p ∧ (p → q) ∧ (s ∨ r) ∧ (r → ¬q)) → (s ∨ t).
Predicate Logic and Quantification
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Predicate Representation:
- Represent the proposition (p(0, 0)∨p(0, 1))∧(p(1, 0)∨p(1, 1)) using quantifiers based on the domain D = {0, 1}.
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Identifying Free Variables:
- Analyze well-formed formulas (wffs) to find any free variables in different logical expressions.
WFF Interpretation
- Translation to English:
- Write an English interpretation of specific well-formed formulas provided in the quiz.
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