### Discrete Mathematics Week 4 NPTEL

**These are the solution of Discrete Mathematics Week 4 NPTEL** **Assignment 4 Answers**

Course name: Discrete Mathematics

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**Q1) Which of the following matrices represent a reflexive relation?**

(A)

(B)

(C)

(D)

(E)

**Answer: C, D, E**

**Q2) A = {srijit, akash, abhi} and B = {shraddha, sanchita} Which of the following subsets belong to A × B?**

(A) {(srijit, sanchita), (abhi, shraddha), (akash, sanchita), (srijit, shraddha)}

(B) {(abhi, shraddha), (akash, shraddha), (sanchita, srijit), (abhi, sanchita)}

(C) {(akash, akash), (akash, shraddha), (srijit, sanchita), (abhi, shrijit)}

(D) {(shrijit, shraddha), (shraddha, shraddha), (shraddha, sanchita), (abhi, shrijit)}**Answer: A**

**Q3) What is the total number of reflexive relations of the set {5,7,13,15}?**

(A) 256

(B) 14

(C) 64

(D) 4096**Answer: (D) 4096**

**These are the solution of Discrete Mathematics Week 4 NPTEL** **Assignment 4 Answers**

**Q4) S = {1,2,3,4,5}. A relation R on set S is defined as R = {(b,a) | 0 ≤ −a + b ≤ 3} What is the cardinality of set R?**

(A) 25

(B) 8

(C) 14

(D) 12**Answer: (C) 14**

**Q5) Let 𝑅 be a relation on a collection of sets defined as follows,𝑅 = {(𝐴,𝐵) | 𝐴 ⊆ 𝐵}Which of the following statement(s) is/are correct?**

(A) 𝑅 is reflexive and transitive

(B) 𝑅 is symmetric

(C) 𝑅 is anti-symmetric

(D) 𝑅 is reflexive but not transitive

**Answer: A, C**

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**These are the solution of Discrete Mathematics Week 4 NPTEL** **Assignment 4 Answers**

**Q6) Let a relation 𝑅 be defined as 𝑅 = {(𝐴, 𝐵) | Both 𝐴 and 𝐵 live in the same city}. Pick out the correct statement(s).**

(A) 𝑅 is anti-symmetric

(B) 𝑅 is reflexive

(C) 𝑅 is transitive

(D) 𝑅 is symmetric**Answer: B, C, D**

**These are the solution of Discrete Mathematics Week 4 NPTEL** **Assignment 4 Answers**

**Q7) Which of the following is an equivalence relation?**

(A) 𝑅 = {(𝑎,𝑏) | both 𝑎 and 𝑏 are even non-zero integers and abab is an integer}

(B) 𝑅 = {(𝑥,𝑦) | 𝑦 − 𝑥 = 0}

(C) R={(1,2),(2,3),(3,4),(4,5),(5,6)}

(D) R={(𝑎,𝑏) | 𝑎 ≤ 𝑏^{3} }**Answer: B**

**Q8) Suppose the cardinality of a set A is 4 and the cardinality of a set B is 3, what are the cardinalities of the cartesian product A × B and the power set of A × B?**

(A) 7 and 128

(B) 12 and 144

(C) 12 and 4096

(D) 7 and 49**Answer: (C) 12 and 4096**

**Q9) Which of the following collection of subsets is a partition of 𝐴 = {1,2,3,4,5}**

(A) {1,2,3},{2,3,4,5}

(B) {4}{2}{3}{1,5}{2,3}

(C) {1,5},{2,3},{4,5}

(D) {1,2}{5}{3,4}**Answer: (D) {1,2}{5}{3,4}**

**These are the solution of Discrete Mathematics Week 4 NPTEL** **Assignment 4 Answers**

**Q10) Let 𝐴 be a set with cardinality 𝑛, and 𝐵 be a set with cardinality 𝑚. There are a total of 64 symmetric relations on 𝐴, and 216 anti-symmetric relations on 𝐵. What is 𝑛 · 𝑚?**

(A) 9

(B) 3

(C) 6

(D) 12**Answer: (A) 9**

**These are the solution of Discrete Mathematics Week 4 NPTEL** **Assignment 4 Answers**

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