The file you uploaded contains a Discrete Mathematics question paper for the BCA program at MIT Vishwaprayag University, dated 17th October 2024. The paper consists of a variety of topics in discrete mathematics, with a total of 40 marks to be completed in 90 minutes. The questions include set theory, functions, relations, recurrence relations, and generating functions.

Here’s a quick breakdown of some of the problems in the paper:

1. Set Theory:

   • Writing sets in roster form.
   • Finding the power set and Cartesian product.
   • Classifying functions (one-one, onto, etc.).
   • Verifying De Morgan's law and the distributive law.

2. Equivalence Relations:

   • Demonstrating that a given relation is an equivalence relation.

3. Inclusion-Exclusion Principle:

   • Determining the number of people who voted in an election using inclusion-exclusion.

4. Recurrence Relations:

   • Fibonacci sequence, Tower of Hanoi.
   • Solving linear and non-linear homogeneous recurrence relations.
   • Finding generating functions.

If you'd like help solving any specific question from the paper, feel free to ask!

Would you like detailed solutions for any of the problems?

Here are five possible directions:

1. How do we solve for the power set and Cartesian product in problem 1(A)(2)?
2. What are equivalence relations, and how do we prove them in set theory?
3. How is the inclusion-exclusion principle applied in elections?
4. Can you explain the recurrence relation for Fibonacci and Tower of Hanoi?
5. What are generating functions, and how are they used to find closed forms?

Tip: In set theory, De Morgan’s laws provide a way to relate the union and intersection of sets through complements.