IGNOU MCS 13 SOLVED ASSIGNMENT

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MCS 13 2025 2026 - English

Course Code : MCS-013 

Course Title : Discrete Mathematics 

Assignment Number : BCA (II)/013/Assignment/2025-26 

Maximum Marks : 100 

Weightage 25% 

Last Date of Submission :  31st October, 2025 (for July Session) 30th April, 2026 (for January Session) 

There are eight questions in this assignment, which carries 80 marks. Rest 20 marks are for viva-voce. Answer all the questions. 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. (a) What is Set? Explain use of Sets in problem solving.

(b) What is a proper subset ? Write the number of proper subsets of the Set 

{2, 3, 4, 5, 6, 7, 8, 9}

(c) Make the truth table for the following.

Here is the transcription of the text and mathematical formulas from the image:

i)

ii)

iii)

(d) Give geometric representation for the following. 

i)

ii)

Q2.

(a) Draw Venn diagram to represent the following. 

i)

ii)

iii)

(b) Write down a suitable mathematical statement that the following symbolic properties can represent.

i)

ii)

(c) Show whether is rational or irrational. 

(d) Explain proof by contradiction with the help of an example. 

Q3.

(a) Explain use of the inclusion-exclusion principle with an example.

(b) Construct logic circuites for the following Boolean expressions:

i) (x+yz) + (yz)' + (z'y)

ii) ( x'y) (xz') (y'z) + xyz

(c) What is a tautology? If P and Q are statements, show whether the statement

is a tautology or not.

(d) Explain the symmetric difference of sets with the help of real-life examples. 

Q4. 

(a) How many words can be formed using the letters of “EXCEPTIONAL”, using each letter at most
once? 

i) If each letter must be used,

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

(b) What is a relation? Explain with an example. What are the different types of relations? Explain with an
example for each. 

Q5.

(a) How many different professional committees of 8 people can be formed, each containing at least 4 Managers, at least 2 Public Servants and 2 IT Professionals from a list of 8 Managers, 6 Public Servants and 8 IT Professionals? 

(b) A and B are mutually exclusive events such that P(A) = 1/3 and P(B) = 1/4 .

Find . What is the probability of , and why? 

(c) What is Pascal’s triangle? Explain. 

(d) Explain how to find the inverse of a function with the help of an example. 

Q6.

(a) How many ways are there to distribute 25 district items into 7 distinct boxes with:

i) At least three empty boxes.

ii) No empty box. 

(b) Explain properties of Set. 

(c) Three Sets A, B and C are: A = {1,7, 8, 9, 13, 15, 17}, B = { 1,2, 3, 4, 5, 6, 8, 9, 10 } and C {1, 2, 3, 5, 7, 9, 10, 11, 13}.

Find ; ; and .

(d) Explain circular permutation with an example. 

Q7.

(a) Compare predicate and proposition logic. 

(b) What is inductive logic? How is it used in problem-solving? Explain with an example.

(c) What is a function? Explain different types of functions with examples. 

(d) Write the following statements in symbolic form: 

(i) Mr. Ravi is thin but healthy.

(ii) Either do not eat unhealthy food or be ready to visit the doctor.

Q8.

(a) Find the inverse of the following functions

(b) What is a Boolean function? Explain with an example.

(c) Show for an integer greater than zero

(d) Write the inverse and contrapositive for these sentences:

(i) If it does not rain, then you will go to market.

(ii) If you are not honest, you are harmful to society.

 

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