Discrete Mathematics Past Paper 2021 PDF

# B.Sc. Information Technology 1st Semester (Batch 2021-24) - APPLIED & DISCRETE MATHEMATICS ## Paper-III ### Exam. Code : 105701 ### Subject Code : 1420 **Time Allowed-3 Hours]** **[Maximum Marks-75** **Note:** - Attempt FIVE questions in all, selecting at least ONE question from each...

# B.Sc. Information Technology 1st Semester (Batch 2021-24) - APPLIED & DISCRETE MATHEMATICS ## Paper-III ### Exam. Code : 105701 ### Subject Code : 1420 **Time Allowed-3 Hours]** **[Maximum Marks-75** **Note:** - Attempt FIVE questions in all, selecting at least ONE question from each Section. The fifth question may be attempted from any Section. All questions carry equal marks. ## Section-A 1. (a) Let A = [1, 3, 4, 5, 6] B = [2, 3, 4, 5, 6, 7] and C = [4, 5, 6, 7, 8]. Find A (BUC), (A∩B) UC. (b) Let A = [1, 2, 3, 4] B = [1, 4, 6, 7] C = [4, 5, 7, 8, 9] Verify (A∪B) UC = AU(BUC). 2. (a) In a group of 400 people, 250 can speak in Hindi and 200 people can speak in English. How many can speak both Hindi and English ? (b) If U = [1, 2, 3, 4, 5, 6, 7, 8, 9] A = [1, 2, 4, 6, 8] B = [1, 3, 5, 7, 8] and C = [2, 3, 4, 5, 7] verify that (AUB) = AB. ## Section-B 3. (a) Using Truth table prove that p^ (qvr) = (p^q) √(p^r) (b) Test the validity of following argument using truth table "if it rain then it will be cold" "if it is cold then I shall stay at home" Since it rains Therefore I shall stay at home. 4. (a) Define following with the help of truth table : (i) Conditional connector; (ii) Biconditional connector; (iii) NAND-Connector (iv) NOR Connector (v) XOR Connector. (b) Prove that (p → qr) = (p → q) → (p → r) with the help of truth table ## Section-C 5. (a) Let B = [1, 2, 3, 6] defined by a + b = 1cm (a,b) a,b = gcd (a,b) a = 6/a show that set B form Boolean Algebra. (b) Reduce the following Boolean expression to complete Sop form: f(x, y, z) = xz° + yz + xyz. ## Section-D 6. (a) Minimize the function : P(A, B, C) = ∑ m (0, 3, 5, 6, 7) + d (2, 4). (b) Prove that (A+B) (Ā+C) = AC+ĀB. 7. (a) If A = [1 0 2 ] [2 0 3] [2 0 3] Prove that A3-6A2 + 7A +21= 0. (b) If A = [1 2 3] [0 2 4] [0 0 5] find inverse of matrix A. 8. (a) Find rank of given matrix if A = [4 3 12] [9 12 15] [-6 -8 -10] (b) Express the following matrix as Sum of Symmetric and skew Symmetric matrix : A = [6 -2 2] [-2 3 -1] [2 -1 3]