Engineering B.E. (Computer Engineering) Sem 3 Discrete Structures and Graph Theory May 2023 Question Paper - Mumbai University | munotes
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Questions asked in this paper
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Q1 a. Define the following with suitable example 5 marks
- b. Check whether [(p>q) “ is a tautology 5
- c. Determine the number of positive integers n where 1< n <100 and n is not divisible by 5
- d. Prove by mathematical induction that 5 2 a Define Equivalence Relation. Let A be a set of integers, Let R be a Relation on AXA 8 defined by (a,b) R (c,d) if and only if ad = bc. Prove that R is an Equivalence Relation
- b. Let A={a, b, c,d, e} 8 Find the transitive closure of it using Warshall’s algorithm c Let G bea group. Prove that the identity element ‘e’ is unique. , 4 3 Prove that set G = {1,2,3,4,5,6} is a finite abelian group of order 6 with respect to 8 the exponential generating function for the sequences 8
- ii) {0,1,0,-1,0,1,0,-1.} c Determine whether the following graphs are isomorphic. Justify your answer. 4 A Function f: R — { — {*}is defined as f(x) = (4x — 5)/(8x 7) Prove that f is Bijective and find the rule b Show that (2,5) encoding function e:B? > by 8 is a group code c Check whether Euler cycle and Euler Path exist in the Graph given below. If yes Mention them 4
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Q5 the Set under multiplication Modulo 7. 8 marks
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Q1 Prove that it is a Cyclic group
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Q2 Find the orders and the Subgroups generated by {2,3}and {3,4} State and explain the extended Pigeonhole principle. How many friends must you have to 8 guarantee that at least five of them will have birthdays in the same month c Functions f,g,h are defined on a set X={a,b,c} as 4
- i) Find fog, gof . Are they equal?
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Q6 a Draw the Hasse Diagram of D72 and and check whether they are Lattice. Define Bounded Lattice and Distributive Lattice. Check if the following diagram is a Distributive 8 Lattice or not c Define the following with suitable example. 4 8 marks
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