Discrete Mathematics | Week 4
Quiz
Link : Discrete Mathematics Week 4 (nptel.ac.in)
1. Which of the following matrices represent a reflexive relation
2. 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)}
3. What is the total number of reflexive relations of the set {5,7,13,15}?
d. 4096
4. 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?
c. 14
5. 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
c. 𝑅 is anti-symmetric
-Answer Reported by Kunal
6. 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).
b. 𝑅 is reflexive
c. 𝑅 is transitive
d. 𝑅 is symmetric
7. Which of the following is an equivalence relation?
b. 𝑅 = {(𝑥,𝑦) | 𝑦 − 𝑥 = 0}
-Explanation Given by 21BCS2601
8. 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?
c. 12 and 4096
9. Which of the following collection of subsets is a partition of 𝐴 = {1,2,3,4,5}?
d. {1,2}{5}{3,4}
10. 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
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