- Discrete Mathematics,

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Are you looking to download a PDF soft copy of the Solved Assignment **MCS-13 - Discrete Mathematics**? Then GullyBaba is the right place for you. We have the Assignment available in English language.

This particular Assignment references the syllabus chosen for the subject of **Computer Application**, for the **July 2023 - January 2024** session. The code for the assignment is MCS-13 and it is often used by students who are enrolled in the MCA, BCA Degree.

Once students have paid for the Assignment, they can Instantly Download to their PC, Laptop or Mobile Devices in soft copy as a PDF format. After studying the contents of this Assignment, students will have a better grasp of the subject and will be able to prepare for their upcoming tests.

Q1. (a) What is Set? Explain use of Set with examples

(b) Make truth table for followings.

(c) Give geometric representation for followings:

i) {5, -3) x ( -2, -2)

ii) {-1, 3) x ( -2, 3)

Q2. (a) Draw Venn diagram to represent followings:

(b) Write down suitable mathematical statement that can be represented by the following symbolic properties.

(c) Show whether β7 is rational or irrational.

Q3. (a) Explain use of inclusion-exclusion principle with example.

(b) Make logic circuit for the following Boolean expressions:

i) (xyz) + (xyz)' + (xz'y)

ii) ( x'yz) (xyz') (xy'z)

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

(π β π) β¨ ( β~ π) is a tautology or not.

Q4. (a) How many words can be formed using letter of βEXCELLENTβ 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? What are different types of relation? Explain equivalence relation with the help of example.

(c) Prove that

(d) What is counterexample? Explain its use with the help of an example.

Q5. (a) How many different professionals committees of 8 people can be formed, each containing at least 2 Doctors, at least 2 Public Servants and 1 IT Expert from list of 7 Doctors, 6 Public Servants and 6 IT Experts?

(b) A and B are mutually exclusive events such that P(A) = 1/2 and P(B) = 1/3 and P (AU B) = 1/4. What is the probability of P(A Υ B)?

(c) Find how many 3 digit numbers are odd?

(d) Explain whether the function f(x) = x + 1 is one-one or not.

Q6. (a) How many ways are there to distribute 21 district items into 6 distinct boxes with:

i) At least two empty box.

ii) No empty box.

(b) Explain principle of multiplication with an example.

(c) Three Sets A, B and C are: A = {1, 2,3,4,5, 8,9,12,15,17}, B = { 1,2, 3 ,4,8,9, 10 } and C {1,2,7, 9, 10, 11, 13}.

Q7. (a) Explain addition theorem in probability.

(b) Make Pascal's triangle up to n = 6.

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

(d) Write the following statements in symbolic form:

(i) Mr. X is poor but happy.

(ii) Either eat healthy food or be ready for poor health.

Q8. (a) Find inverse of the following functions

Q1. (a) State and explain De Morganβs laws for Boolean algebra.

(b) Make truth table for followings.

(c) Give geometric representation for followings:

i) {5, 5) x ( -2, -2)

ii) {1, 5) x ( -2, -3)

Q2. (a) Draw Venn diagram to represent followings:

(b) Write down suitable mathematical statement that can be represented by the following symbolic properties.

(c) Show whether β5 is rational or irrational.

Q3. (a) Explain inclusion-exclusion principle with example.

(b) Make logic circuit for the following Boolean expressions:

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

ii) ( x'yz') (xyz') (x'y'z)

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

(π β π) β¨ ( β π) is a tautologyor not.

Q4. (a) How many words can be formed using letter of PEPSUDENT using each letter at most once?

i) If each letter must be used,

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

(b) Show that:

Q => P and (~Q β¨ P) are equivalent.

(c) Prove that

(d) Explain principal of duality with the help of example

Q5. (a) How many different professionals committees of 10 people can be formed, each containing at least 2 Professors, at least 3 Managers and 3 ICT Experts from list of 10 Professors, 6 Managers and 8 ICT Experts?

(b) A and B are mutually exclusive events such that P(A) = 1/4 and P(B) = 2/5 and P (AU B) = 1/2. What is the probability of P(A Υ B)

(c) Explain addition theorem in probability

Q6. (a) How many ways are there to distribute 15 district item into 5 distinct boxes with:

i) At least two empty box.

ii) No empty box.

(b) Explain principle of multiplication with an example

(c) Three Sets A, B and C are: A = {1, 2, 8,9,12,15,17}, B = { 1,2, 3 ,4, 10 } and C {7, 9, 10, 11, 13}.

Q7. (a) Find how many 3 digit numbers are even?

(b) A coin is tossed n times. What is the probability of getting exactly p tails?

(c) What is a function? Explain following types of functions with example.

i) Surgective

ii) Injective

iii)Bijective

(d) Write the following statements in symbolic form:

(a) Shyam is rich but unhappy

(b) Either do physical exercise or be ready for poor health

Q8. (a) Find inverse of the following function:

What is a relation? Explain equivalence relation with the help of an example.

(b) Find dual of Boolean Expression for the output of the following logic circuit.

(c) Explain Logical Connectives and Logical Quantifiers with the help of examples.

- University IGNOU (Indira Gandhi National Open University)
- Title Discrete Mathematics
- Language(s) English
- Session July 2023 - January 2024
- Code MCS-13
- Subject Computer Application
- Degree(s) MCA, BCA
- Course Core Courses (CC)
- Author Gullybaba.com Panel
- Publisher Gullybaba Publishing House Pvt. Ltd.

The IGNOU open learning format requires students to submit study Assignments. Here is the final end date of the submission of this particular assignment according to the university calendar.

**30th April**Β (if Enrolled in the June Exams)**31st October**(if Enrolled in the December Exams).

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- July 2023 - January 2024 24 Pages (0.00 ), PDF Format SKU: IGNGB-AS-BCA-MCS13-EN-379

- July 2022 - January 2023 29 Pages (0.00 ), PDF Format SKU: IGNGB-AS-BCA-MCS13-EN-231

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