IGNOU MCS 212 SOLVED ASSIGNMENT

Included:

MCS 212 (January 2025 - July 2025) - ENGLISH

Course Code:MCS-212

Course Title:Discrete Mathematics

Assignment Number:MCA_NEW(I)/212/Assign/2025

Maximum Marks:100

Weightage:30%

Last Dates for Submission:30th April 2025 (for January Session)

31st October 2025 (for July Session)

This assignment has 20 questions of 4 Marks each, amounting to 80 marks. Answer all questions. Rest 20 marks are for viva voce. You may use illustrations and diagrams to enhance the explanations. Please go through the guidelines regarding assignments given in the Programme Guide for the format of presentation.

,Q1: Prove by mathematical induction that

Q2: Verify whether √11 is rational or irrational.

Q3: Write the following statements in the symbolic form.

i) Some students can not appear in exam.

ii) Everyone can not sing.

Q4: Draw logic circuit for the following Boolean Expression:

Q5: Explain whether function: f(x) = x² posses an inverse function or not.

Q6: Write the finite automata corresponding to the regular expression (a + b)*ab

Q7: If L1 and L2 are context free languages then, prove that L1 U L2 is a context free language.

Q8: Explain Decidable and Undecidable Problems. Give example for each.

Q9: What is equivalence relation? Explain use of equivalence relation with the help of an example.

Q10: There are three Companies, C1, C2 and C3. The party C1 has 4 members, C2 has 5 members and C3 has 6 members in an assembly. Suppose we want to select two persons, both from the same Company, to become president and vice president. In how many ways can this be done?

Q11: How many words can be formed using letter of DEPARTMENT using each letter at most once?

i) If each letter must be used,

ii) If some or all the letters may be omitted.

Q12: What is the probability that a number between 1 and 10,000 is divisible by neither 2, 3, 5 nor 7?

Q13: Explain inclusion-exclusion principle and Pigeon Hole Principle with example.

Q14: Find an explicit recurrence relation for minimum number of moves in which the n-disks in tower of Hanoi puzzle can be solved! Also solve the obtained recurrence relation through an iterative method.

Q15: Find the solution of the recurrences relation 

Q16: Prove that the complement of  is G

Q17: What is a chromatic number of a graph? What is a chromatic number of the following graph?

Q18: Determine whether the above graph has a Hamiltonian circuit. If it has, find such a circuit. If it does not have, justify it.

Q19: Explain and prove the Handshaking Theorem, with suitable example

Q20: Explain the terms PATH, CIRCUIT and CYCLES in context of Graphs

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