# Discrete Mathematics Week 4 NPTEL

### These are the solution of Discrete Mathematics Week 4 NPTELAssignment 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)

Q2) A = {srijit, akash, abhi} and B = {shraddha, sanchita} Which of the following subsets belong to A ร B?
(C) {(akash, akash), (akash, shraddha), (srijit, sanchita), (abhi, shrijit)}

Q3) What is the total number of reflexive relations of the set {5,7,13,15}?
(A) 256
(B) 14
(C) 64
(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 โa + b โค 3} What is the cardinality of set R?
(A) 25
(B) 8
(C) 14
(D) 12

Q5) Let ๐ be a relation on a collection of sets defined as follows,
๐ = {(๐ด,๐ต) | ๐ด โ 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

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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

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,๐) | both ๐ and ๐ are even non-zero integers and abab is an integer}
(B) ๐ = {(๐ฅ,๐ฆ) | ๐ฆ โ ๐ฅ = 0}
(C) R={(1,2),(2,3),(3,4),(4,5),(5,6)}
(D) R={(๐,๐) | ๐ โค ๐3 }

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

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}

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. There are a total of 64 symmetric relations on ๐ด, and 216 anti-symmetric relations on ๐ต. What is ๐ ยท ๐?
(A) 9
(B) 3
(C) 6
(D) 12