GTU BE 2020 Summer Question Papers || Gujarat Technological University
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GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- IV EXAMINATION - SUMMER 2020
Subject Code: 3140708 Date:29/10/2020
Subject Name: Discrete Mathematics
Time: 10:30 AM TO 01:00 PM Total Marks: 70
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Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
| Marks | |
|---|---|
| Q.1 (a) If A={a, b} and B={c, d} and C = {e, f} then find (i) (A x B) U (B x C) (ii) A x (B U C). | 03 |
| (b) Define even and odd functions. Determine whether the function f: R ? R defined by f(x)=2x+7 is one-to-one or bijective. | 04 |
| (c) (i) Show that the relation x = y (mod m) defined on the set of integers Z is an equivalence relation. | 03 |
| (ii) Draw the Hasse diagram for the partial ordering {(A,B) | A ? B} on the power set P(S), where S = {a,b,c}. | 04 |
| Q.2 (a) Define equivalence class. Let R be the relation on the set of integers Z defined by (x — y) is an even integer, find the disjoint equivalence classes | 03 |
| (b) A committee of 5 persons is to be formed from 6 men and 4 women. In how many ways can this be done when (i) at least 2 women are included (ii) at most 2 women are included ? | 04 |
| (c) Solve the recurrence relation an +5an-1 +6an-2 =3n2 using the method of undetermined coefficients. | 07 |
| OR | |
| (c) Solve the recurrence relation using the method of generating function an—5an-1 +6an-2=3n, n=2, a0=0, a1=2. | 07 |
| Q.3 (a) Define simple graph, degree of a vertex and complete graph. | 03 |
| (b) Define tree. Prove that there is one and only one path between every pair of vertices in a tree T. | 04 |
| (c) (i) A graph G has 15 edges, 3 vertices of degree 4 and other vertices of degree 3. Find the number of vertices in G. | 03 |
| (ii) Define vertex disjoint and edge disjoint subgraphs by drawing the relevant graphs. | 04 |
| OR | |
| Q.3 (a) Show that (G, +5) is a cyclic group, where G={0, 1, 2, 3, 4 }. | 03 |
| (b) Define the following by drawing graphs (i) weak component (ii) unilateral component (iii) strong component. | 04 |
| (c) (i) Construct the composite tables for (i) addition modulo 4 and (ii) multiplication modulo 4 for Z4 ={0,1,2,3}. Check whether they have identity and inverse element. | 03 |
| (ii) Define ring. Show that the set M = { This download link is referred from the post: GTU BE 2020 Summer Question Papers || Gujarat Technological University --- Content provided by FirstRanker.com --- |