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A

Section A: Long Answer Questions

Attempt any TWO questions.

3 questions·10 marks each
1long10 marks

Define a set. Explain set operations with Venn diagrams. State and prove the principle of inclusion-exclusion for two and three sets.

setsinclusion-exclusion
2long10 marks

What is a Boolean algebra? Explain Boolean functions. Minimize the Boolean function (F(x,y,z) = \Sigma(0,2,4,6)) using a Karnaugh map.

boolean-algebrakmap
3long10 marks

Define permutation and combination. In how many ways can the letters of the word 'COMPUTER' be arranged? How many of these arrangements begin with a vowel?

countingpermutation
B

Section B: Short Answer Questions

Attempt any EIGHT questions.

9 questions·5 marks each
4short5 marks

Construct the truth table for (p \oplus q) (exclusive or).

logic
5short5 marks

Define floor and ceiling functions with examples.

functions
6short5 marks

What is a multiset? Give an example.

sets
7short5 marks

Find the gcd of 252 and 198 using the Euclidean algorithm.

number-theory
8short5 marks

Define weighted graph and give a real-life application.

graph
9short5 marks

What is a spanning tree? How many spanning trees does (K_3) have?

tree
10short5 marks

State the conditions for a graph to be Eulerian.

graph
11short5 marks

Define a Boolean expression and simplify (x + x'y).

boolean-algebra
12short5 marks

How many ways can 5 people be seated around a circular table?

counting