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

• Thursday, September 08, 2016
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December-2007
CS-203/204
DISCRETE STRUCTURES
B.Tech. 3rd 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 ar-7a, +10ar-2 =0, given that an =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 (B C). For any sets A.B.C.

9.     Minimize the following switching function 