DSTL Unit 3 Notes AKTU (BCS303)

AKTU · BTECH · Semester 3 · Discrete Structures & Theory of Logic · Unit 3 · Notes

AKTU Discrete Structures & Theory of Logic (BCS303) Unit 3 notes for B.Tech Semester 3 – Theory of Logic. Topics: Propositional Logic, Theory of Inference…

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Unit 3: Theory of Logic – AKTU syllabus topics

  • Propositional Logic
  • Theory of Inference
  • Predicate Logic

Most asked AKTU PYQ questions from Unit 3

  1. Q6a. Prove the validity of the following argument. If Mary runs for office, She will be elected. If Mary attends the meeting, she will run for office. Either Mary will attend the meeting or she will go to India. But Mary cannot go to India. “Thus Mary will be elected”. (10 marks, 2022-23)
  2. Q5a. Define Modular Lattice. Justify that if ‘a’ and ‘b’ are the elements in a bounded distributive lattice and if ‘a’ has complement a′. then I) a ˅ (a′˄ b)=a˅ b II ) a˄ (a′˅ b)=a˄ b (10 marks, 2021-22)
  3. Q5b. i) Justify that (D36, \) is lattice. ii) Let L1 be the lattice defined as D6 and L2 be the lattice (P(S), ≤), where P(S) be the power set defined on set S= {a, b}. Justify that the two lattices are isomorphic. (10 marks, 2021-22)
  4. Q2c. Prove that in any lattice the following distributive inequalities hold: i. a ˄ (b ˅ c) ≥ (a ˄ b) ˅ (a ˄ c), ii. a ˅ (b ˄ c) ≤ (a ˅ b) ˄ (a ˅ c) (10 marks, 2020-21)
  5. Q5a. Let (L,∨,∧,≤) be a distributive lattice and a,b∈L. if a∧b=a∧c and a∨b=a∨c then show that b=c (10 marks, 2019-20)
  6. Q6b. Prove the validity of the following argument “if the races are fixed so the casinos are crooked, then the tourist trade will decline. If the tourist trade decreases, then the police will be happy. The police is never happy. Therefore, the races are not fixed. (10 marks, 2019-20)
  7. Q5a. Test the validity of the following argument. “If there was a ball game, then traveling was difficult. If they arrived on time, then traveling was not difficult. They arrived on time. Therefore, There was no ball game.” (7 marks, 2023-24)
  8. Q1f. If L be a lattice, then for every a and b in L prove that a ˄ b = a if and only if a ≤ b. (2 marks, 2020-21)
  9. Q6b. Convert the following two statements in quantified expressions of predicate logic (i) For every number there is a number greater than that number. (ii) Sum of every two integer is an integer. (iii) Not Every man is perfect. (iv) There is no student in the class who knows Spanish and German (10 marks, 2022-23)
  10. Qc. Translate the following statements in symbolic form: (i) The sum of two positive integer is always positive. (ii) Everyone is loved by someone. (iii) Some people are not admired by everyone. (iv) If a person is female and is a parent, then this person is someone’s mother. (7 marks, 2025-26)

AKTU paper codes: BCS303, KCS303, BCS303H, KCS303H

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