Discrete Structures Question Paper of 3rd Semester CSE74 Download Previous Years Question Paper 6

December-2007

CS-203/204

DISCRETE STRUCTURES

B.Tech. 3^rd Semester-2127

Note: Section –A is compulsory. Attempt any four question from section-B.A attempt any two questions from section –C.

Section –A

1.      

a.     State Euler’s formula for connected planar graph.

b.     Define Hamiltonian cycle.

c.      What is a circular permutation of n objects & how many are there?

d.     State principle of inclusion & Exclusion.

e.       Find the power set P(A) of A-{1,2,3}.

f.       What is an equivalence relation?

g.     Define Normal subgroup.

h.     Define isomorpltism of groups.

i.       Define Improper ideal.

j.       Define Quotient Ring.

Section-B

2.     State  Euler & Hamiltonian paths with maps.

3.     Solve the recurrence relation a_r-7a, +10a_r-2 =0, given that a_n =0, a₁=3 

4.     If H & K are two subgroup of a group (G.). prove that H K  is subgroup of G

5.     Minimize the Boolean expression F = xyz x’yz’ xyz’.

6.     Prove that “congruence modulo H, a = b(modH) “ is an equivalence relation in G.

Section –C

7.       

a.     Prove that the Kernel fo a Homomorphism f form (G,) to group (G,) us a normal subgroup o (G,.)

b.     State Lagrange’s theorem on finite groups.

8.       

a.     If A is any set, then (A’)’ = A.

b.     Prove that (A B) C = A (BC). For any sets A.B.C.

9.     Minimize the following switching function