# 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**