Browse papers
A

Section A: Long Answer Questions

Attempt any TWO questions.

3 questions·10 marks each
1long10 marks

Define lattice. Explain partially ordered sets (poset) and draw a Hasse diagram for the divisibility relation on the set {1, 2, 3, 6, 12, 24, 36}. Identify the maximal, minimal, greatest and least elements.

latticeposet
2long10 marks

What is generating function? Use generating functions to solve the recurrence relation (a_n = 3a_{n-1} + 2) with (a_0 = 1).

generating-functionrecurrence
3long10 marks

Explain Euler and Hamiltonian paths and circuits with examples. State the necessary and sufficient conditions for the existence of an Euler circuit in a connected graph.

grapheuler-hamiltonian
B

Section B: Short Answer Questions

Attempt any EIGHT questions.

9 questions·5 marks each
4short5 marks

Differentiate between proof by contradiction and proof by contraposition.

proof
5short5 marks

Define the inverse and identity functions.

functions
6short5 marks

What is the symmetric difference of two sets? Give an example.

sets
7short5 marks

Define a poset and Hasse diagram.

relations
8short5 marks

State Dijkstra's algorithm in brief.

graph
9short5 marks

What is a rooted tree? Define the height of a tree.

tree
10short5 marks

Define a cyclic group with an example.

algebraic-structures
11short5 marks

Use the Euclidean algorithm to find gcd(414, 662).

number-theory
12short5 marks

Find the coefficient of (x^5) in ((1+x)^{10}).

counting