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

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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

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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

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

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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

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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

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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

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

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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 ≤ 𝑏³ }
Answer: B

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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

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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}

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

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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

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

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