Discrete Structures Question Paper of 3rd Semester CSE74 Download Previous Years Question Paper 18

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Total No. of Questins:9]

B.Tech. (Sem. – 3^rd )

DISCRETE STRUCTURES

SUBJECT CODE : CS - 203

Paper ID : [A0452]

Time : 03 Hours

Instruction to Candidates:

1) Section - A is Compulsory.

2) Attempt any Four questions from Section - B.

3) Attempt any Two questions from Section - C.

Section - A

1.       

a.     Define function and relation. Give example of each.

b.     Define semi group and Monoid.

c.      Prove that ⁿ⁺¹C_r =ⁿC_r-1 +ⁿCr

d.     Find ‘n’ if P(n,2)= 72

e.      What is Eulerian graph. Give example.

f.       Define one-one and onto function. Give example.

g.     What is Ring Homomorphism.

h.     Define Permutation. How many permutations are possible on a set S = (1,2,3,4,5).

i.       Find the product of the following permutations

 

j.       Give an example of equivalence relation.

Section –B

2.     State and prove D’Morgan’s law.

3.     Prove that Inclusion relation on the set of sets is and equivalence relation.

4.     Suppose f : G → G’ is a group homomorphism. Prove that f(e)= e’ and f(a^-1) = f(a^)-1

5.     Prove that V-E +R =2, where Vis the number of vertices, E the number of edges and R the number of regions in a graph.

6.     Let A = {1,2,3,4,6,8,9,12,18,24} be ordered by the relation “x” divides “y”. draw Hasse diagram of this relation.

Section –C

7.     Express the output Y as a Boolean expression in the inputs A, B,C  for the logic circuits in the following figure.

8.     A bag contains six white marbles and five red marbles. Find the number of ways four marbles can be drawn from the bag if.

a.     They can be any color.

b.     Two must be white and two red.

9.     Let X = {1,2,---- 8,9}.determine whether or not each of the following is a partition of X.

a.     [{1,3,6},{2,8},{5,7,9}]

b.     [{1,5,7}, {2,4,8,9},{3,5,6}]