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## Discrete Structures Question Paper of 3rd Semester CSE74 Download Previous Years Question Paper 2

• Thursday, September 08, 2016
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December-2003
CS-203/204
DISCRETE STRUCTURES
B.Tech. 3rd Semester-2123
Note: Section –A is compulsory. Attempt any four question from section-B.A attempt any two questions from section –C.
Section –A
1.
a.     Differentiate between a directed and undirected graph.
b.     Define a simple path and a trail in a graph.
c.      What is a trivial graph?
d.     Define isomorphic graph.
e.      Explain the fundamental principle of counting.
f.       State inclusion and Exclusion principle.
g.     What is a ring?
h.     What are cosets? Explain langrage’s theorem.
i.       What is meant by tautology?
j.       What is a power set?
Section –B

2.     Consider four vowels and eight consonants. Find the number m of five letter words containing two different vowels  and three different consonants that can be formed from the given letters.

3.     Let A,B,C be arbitrary sets, prove that A-(B-C)=A-(B U C)

4.     If an undirected graph which is connected and has zero or exactly 2 vertices of odd degree. Show that it has an Euler path.

5.     Let S be a semi group with an identity element e and suppose b and b’ are inverse of an element a in S, show that b =b

6.     What are rings, integral domains and fields? State each o them with an example

Section –C

7.     Prove that if A,B,C,D are arbitrary sets, then 8.     What is an Eulerian circuit? Prove that an undirected graph G possesses an Eulerian circuit if and only if it is connected and its vertices are all of even degree.

9.     Let E = xy+ xyz +x’yz. Prove that xz’ + E=E