DSTL Unit 2 Notes AKTU (BCS303)

AKTU · BTECH · Semester 3 · Discrete Structures & Theory of Logic · Unit 2 · Notes

AKTU Discrete Structures & Theory of Logic (BCS303) Unit 2 notes for B.Tech Semester 3 – Functions & Boolean Algebra. Topics: Functions, Growth of…

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Unit 2: Functions & Boolean Algebra – AKTU syllabus topics

  • Functions
  • Growth of Functions
  • Boolean Algebra: Karnaugh Maps (K-Map)

Most asked AKTU PYQ questions from Unit 2

  1. Q5b. Solve the following Boolean functions using K-map: (i) F(A,B,C,D) = ∑( m0, m1, m2, m4, m5, m6, m8, m9, m12, m13, m14 ) (ii) F(A,B,C,D)=∑(0,2,5,7,8,10,13,15) (10 marks, 2022-23)
  2. Q2b. Solve the following Boolean function using K-map: F(A, B, C) = (1, 2, 5, 7) and D(0, 4, 6) using SOP. (7 marks, 2024-25)
  3. Q4a. Solve the following Boolean functions using K-map: (i) F(A, B, C, D) = ∑(m0, m1, m2, m4, m5, m6, m8, m9, m12, m13, m14 ) (ii) F(A, B, C, D) = ∑(0, 2, 5, 7, 8, 10, 13, 15) (7 marks, 2024-25)
  4. Q2b. Solve the following Boolean functions using K-map: (i) F(A,B,C,D) = ∑ (m0,m1,m2,m4,m5,m6,m8,m9,m12,m13,m14) (ii) F(A,B,C,D) = ∑ (0,2,5,7,8,10,13,15) (7 marks, 2023-24)
  5. Q4a. Solve the following Boolean function using K-map: F(A,B,C) = (1,2,5,7) and D(0,4,6) using SOP. (7 marks, 2023-24)
  6. Q4a. Define the binary operation * on Z by x*y=x + y + 1 for all x,y belongs to set of integers. Verify that (Z,*) is abelian group? Discuss the properties of abelian group. (10 marks, 2021-22)
  7. Q4b. i) Justify that “The intersection of any two subgroup of a group (G,*) is again a subgroup of (G,*)”. ii) Justify that “If a,b are the arbitrary elements of a group G then (ab)^2 = a^2b^2 if and only if G is abelian. (10 marks, 2021-22)
  8. Q4b. Prove or disprove that intersection of two normal subgroups of a group G is again a normal subgroup of G. (10 marks, 2019-20)
  9. Q1d. Calculate the composite mapping gof if f: R→ R is given by f(x) = ex and g: R → R is given by g(x) = sin x. (2 marks, 2024-25)
  10. Q1d. Find the composite mapping gof if f: R→R is given by f(x) = ex and g: R→R is given by g(x) = sinx (2 marks, 2022-23)

AKTU paper codes: BCS303, KCS303, BCS303H, KCS303H

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