Discrete Mathematics Model Question Paper April 2025 | MSU B.Sc Computer Science Semester 2

University: Manonmaniam Sundaranar University

This Discrete Mathematics model question paper is based on the latest syllabus for B.Sc Computer Science Semester 2 students.

Course: B.Sc. Computer Science
Semester: II
Subject: Discrete Mathematics
Time: 3 Hours
Maximum Marks: 75

---

✨ PART – A (10 × 1 = 10 Marks)

Answer All Questions

1. Which of the following is a subset of every set?
   • a) Universal set
   • b) Empty set
   • c) Power set
   • d) Singleton set
2. If A = {1, 2, 3}, then the power set P(A) has how many elements?
   • a) 6
   • b) 3
   • c) 9
   • d) 8
3. If (a, b) ∈ R ⇒ (b, a) ∈ R, then the relation is:
   • a) Reflexive
   • b) Transitive
   • c) Symmetric
   • d) Antisymmetric
4. The inverse of the relation R = {(1, 2), (2, 3)} is:
   • a) {(1, 2), (2, 3)}
   • b) {(3, 2), (2, 1)}
   • c) {(2, 2), (3, 3)}
   • d) {(2, 1), (3, 2)}
5. The function f(x) = x + 1 from integers to integers is:
   • a) Injective only
   • b) Surjective only
   • c) Bijective
   • d) Neither injective nor surjective
6. If f(x) = x + 2, then its inverse is:
   • a) f⁻¹(x) = x − 2
   • b) f⁻¹(x) = x + 2
   • c) f⁻¹(x) = 1 − x
   • d) f⁻¹(x) = 2x
7. Which of the following is a tautology?
   • a) P ∧ ¬P
   • b) P ∨ ¬P
   • c) P → ¬P
   • d) P ∧ Q
8. What is the truth value of P → P?
   • a) True
   • b) False
   • c) Undefined
   • d) None of the above
9. Which matrix satisfies A = A^T?
   • a) Skew-symmetric matrix
   • b) Symmetric matrix
   • c) Identity matrix
   • d) Diagonal matrix
10. Which is a property of transpose of matrices?
    • a) (A^T)^T = A
    • b) (A + B)^T = A^T + B^T
    • c) (AB)^T = B^TA^T
    • d) All of the above

---

✨ PART – B (5 × 5 = 25 Marks)

Answer All Questions (Either OR)
Answer should not exceed 250 words

11. a) Define power set with an example
    OR
    b) If A = {1, 2, 3}, B = {3, 4}, C = {4, 5, 6}, find A × (B ∪ C)
12. a) Explain closure operations on relations
    OR
    b) Find the reflexive closure of R = {(a, a), (a, b), (b, c), (c, a)} on A = {a, b, c}
13. a) List the classification of functions
    OR
    b) Let f: R → R defined by f(x) = 5x + 1. Find f^-1
14. a) Describe tautology with example
    OR
    b) Prove: (P → (Q → R)) ⇒ ((P → Q) → (P → R))
15. a) Describe operations on matrices
    OR
    b) Define symmetric and skew-symmetric matrices with examples

---

✨ PART – C (5 × 8 = 40 Marks)

Answer All Questions (Either OR)
Answer should not exceed 500 words

16. a) Describe operations on sets with examples
    OR
    b) Prove: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
17. a) Describe classifications of relations
    OR
    b) Let A = {1, 2, 3}, R = {(1,2), (1,3), (2,3)}. Determine matrix MR
18. a) Explain composite and inverse functions with examples
    OR
    b) Define functions with an example problem
19. a) Prove: A = (P → (Q → R)) → ((P → Q) → (P → R))
    OR
    b) Construct truth table for:
    A = (P ∧ Q) ∨ (¬P ∧ Q) ∨ (P ∧ ¬Q) ∨ (¬P ∧ ¬Q)
20. a) Find determinant of matrix:
    
    

    1	2	3
    4	5	6
    7	8	9

    
    OR
    b) Explain different types of matrices with examples

---