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)

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

(B)

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

(C)

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

(D)

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

(E)

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

Answer: C, D, E


Q2) A = {srijit, akash, abhi} and B = {shraddha, sanchita} Which of the following subsets belong to A ร— 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 โ‰ค โˆ’a + b โ‰ค 3} What is the cardinality of set R?
(A) 25
(B) 8
(C) 14
(D) 12
Answer: (C) 14


Q5) Let ๐‘… be a relation on a collection of sets defined as follows,
๐‘… = {(๐ด,๐ต) | ๐ด โІ ๐ต}
Which of the following statement(s) is/are correct?

(A) ๐‘… is reflexive and transitive
(B) ๐‘… is symmetric
(C) ๐‘… is anti-symmetric
(D) ๐‘… 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 ๐‘… be defined as ๐‘… = {(๐ด, ๐ต) | Both ๐ด and ๐ต live in the same city}. Pick out the correct statement(s).
(A) ๐‘… is anti-symmetric
(B) ๐‘… is reflexive
(C) ๐‘… is transitive
(D) ๐‘… 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) ๐‘… = {(๐‘Ž,๐‘) | both ๐‘Ž and ๐‘ are even non-zero integers and abab is an integer}
(B) ๐‘… = {(๐‘ฅ,๐‘ฆ) | ๐‘ฆ โˆ’ ๐‘ฅ = 0}
(C) R={(1,2),(2,3),(3,4),(4,5),(5,6)}
(D) R={(๐‘Ž,๐‘) | ๐‘Ž โ‰ค ๐‘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 ร— B and the power set of A ร— 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 ๐ด = {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 ๐ด be a set with cardinality ๐‘›, and ๐ต be a set with cardinality ๐‘š. There are a total of 64 symmetric relations on ๐ด, and 216 anti-symmetric relations on ๐ต. What is ๐‘› ยท ๐‘š?
(A) 9
(B) 3
(C) 6
(D) 12
Answer: (A) 9


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