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A

Section A: Long Answer Questions

Attempt any TWO questions.

3 questions·10 marks each
1long10 marks

Define logical equivalence. Using laws of logic (without truth table), show that (\neg(p \lor (\neg p \land q))) is logically equivalent to (\neg p \land \neg q).

logicequivalence
2long10 marks

What is a function? Explain one-to-one, onto and bijective functions with examples. When does the inverse of a function exist? Find the inverse of (f(x) = 2x + 3).

functionsinverse
3long10 marks

Explain Dijkstra's algorithm for finding the shortest path in a weighted graph. Apply it to find the shortest path from a source vertex to all other vertices in a given example graph.

graphshortest-path
B

Section B: Short Answer Questions

Attempt any EIGHT questions.

9 questions·5 marks each
4short5 marks

Define quantifiers with examples.

quantifiers
5short5 marks

What is a recursive function? Give an example.

functions
6short5 marks

Define cardinality of a set. What are countable and uncountable sets?

sets
7short5 marks

State and explain the addition and multiplication rules of counting.

counting
8short5 marks

Define isomorphic graphs with an example.

graph
9short5 marks

What is a binary search tree? Give an example.

tree
10short5 marks

Prove that the sum of degrees of all vertices in a graph is even.

graph
11short5 marks

Define modular arithmetic. Compute (17 \bmod 5) and (-7 \bmod 3).

number-theory
12short5 marks

State the rules of inference: modus ponens and modus tollens.

inference