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A

Section A: Long Answer Questions

Attempt any TWO questions.

3 questions·10 marks each
1long10 marks

Define proposition. Construct the truth table for the compound proposition ((p \rightarrow q) \leftrightarrow (\neg q \rightarrow \neg p)) and determine whether it is a tautology.

logictruth-table
2long10 marks

What is mathematical induction? Using the principle of mathematical induction, prove that (1 + 2 + 3 + \dots + n = n(n+1)/2) for all positive integers n.

inductionproof
3long10 marks

Define a graph. Explain the different types of graphs with examples. Describe the adjacency matrix and incidence matrix representation of a graph.

graphrepresentation
B

Section B: Short Answer Questions

Attempt any EIGHT questions.

9 questions·5 marks each
4short5 marks

Convert the decimal number 245 into binary, octal and hexadecimal.

number-system
5short5 marks

Define conjunction, disjunction and negation with truth tables.

logic
6short5 marks

What is a bijective function? Give an example.

functions
7short5 marks

State the principle of inclusion and exclusion.

sets
8short5 marks

Explain the difference between a walk, path and circuit in a graph.

graph
9short5 marks

Define equivalence relation with an example.

relations
10short5 marks

Solve the recurrence relation (a_n = 2a_{n-1}), (a_0 = 3).

recurrence
11short5 marks

What is a planar graph? State Euler's formula for planar graphs.

graph
12short5 marks

Find the number of ways to select 3 students from a group of 10.

counting