# Discrete Mathematics | Week 4

## Quiz

1. Which of the following matrices represent a reflexive relation

Explanation

2. A = {srijit, akash, abhi} and B = {shraddha, sanchita} Which of the following subsets belong to A × B?

Explanation

3. What is the total number of reflexive relations of the set {5,7,13,15}?

d. 4096

Explanation

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

Explanation

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

Explanation

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

Explanation

7. Which of the following is an equivalence relation?

b.   𝑅 = {(𝑥,𝑦) | 𝑦 − 𝑥 = 0}

Explanation

-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

Explanation

9. Which of the following collection of subsets is a partition of 𝐴 = {1,2,3,4,5}?

d. {1,2}{5}{3,4}

Explanation

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

Explanation  