Discrete Mathematics Model Question Paper PDF

SET – C FACULTY OF SCIENCE/FACULTY OF COMMERCE & BUSINESS MANAGEMENT SEMESTER END EXAMINATIONS COURSE- SEMESTER SUBJECT – PAPER. NO. Time: 11/2 Hrs] [Max. Marks:20...

SET – C FACULTY OF SCIENCE/FACULTY OF COMMERCE & BUSINESS MANAGEMENT SEMESTER END EXAMINATIONS COURSE- SEMESTER SUBJECT – PAPER. NO. Time: 11/2 Hrs] [Max. Marks:20 Section – A Answer any six questions. 6 x 2 = 12 1. Express the statement in the form of a logical expression: “ The sum of two positive integers is always positive” and explain the terms in the expression. 2. Prove the statement: If there are 100 students enrolled in this course this semester, then 62 = 36. 3. The number of square tiles around a pool generates an arithmetic sequence as follows: …. How many tiles would there be around a pool of width 30? 4. In a certain culture, the count of bacteria gets doubled after every hour. There were 3 bacteria in the culture initially. What would be the total count of bacteria at the end of the 6th hour? 5. Draw a venn diagram and shade the area represented by A∪(B∩C)c 6. If f(x) = x + 5 and g(x) = 1/ (2x + 5), then what is the value of [(f x g)(5)]? 7. Consider the relation R from X to Y X = {1, 2, 3}, Y = {8, 9} R = {(1, 8) (2, 8) (1, 9) (3, 9)} Find the complement relation of R. 8. Find the domain and range of the relation R = {(1,2), (2,3), (3,4), (4,5)}. 9. What is a fallacy? Give an example for a fallacy? 10. Show that if A ⊆ B and B ⊆ C then A ⊆ C Section – B Answer any two questions. 2x4=8 11. How many elements are present in the set S if S is defined as  S = {x ∈ R : x ≥ 0 and 2|√x − 3|+ √x (√x − 6) + 6 = 0} 12. Is the implication operation in Propositional Logic associative? That is, is it always the case that (p → q) → r = p → (q → r) ? Prove or disprove. 13. Prove that for any integer k, the result of 3k2 + k is even. 14. If R ={(x,y) ∣ x is a multiple of y} which properties does R obey? (Transitive, Reflexive, Symmetric, & Anti-symmertic)