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A

Section A: Long Answer Questions

Attempt any TWO questions.

3 questions·10 marks each
1long10 marks

What are rules of inference? Show that the premises (p \rightarrow q), (q \rightarrow r) and (p) lead to the conclusion r using rules of inference.

inferencelogic
2long10 marks

Define recurrence relation. Solve the recurrence relation (a_n = 5a_{n-1} - 6a_{n-2}) with initial conditions (a_0 = 1) and (a_1 = 0).

recurrencesolving
3long10 marks

Define tree and spanning tree. Explain Kruskal's algorithm to find a minimum spanning tree with a suitable example.

treespanning-tree
B

Section B: Short Answer Questions

Attempt any EIGHT questions.

9 questions·5 marks each
4short5 marks

Show that (p \rightarrow q) is logically equivalent to (\neg p \lor q).

logic
5short5 marks

Define power set. Write the power set of {a, b, c}.

sets
6short5 marks

What is a partial order relation? Give an example.

relations
7short5 marks

State the pigeonhole principle with an example.

counting
8short5 marks

Define complete graph and bipartite graph.

graph
9short5 marks

Find the number of edges in a complete graph with 6 vertices.

graph
10short5 marks

Define a tree and state its basic properties.

tree
11short5 marks

What is a tautology and a contradiction? Give one example of each.

logic
12short5 marks

Define the composition of two functions with an example.

functions