1. Which of the following matrices represent a reflexive relation?

CORRECT ANSWER

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

• • • {(srijit, sanchita), (abhi, shraddha), (akash, sanchita), (srijit, shraddha)}

    • {(abhi, shraddha), (akash, shraddha), (sanchita, srijit), (abhi, sanchita)}

    • {(akash, akash), (akash, shraddha), (srijit, sanchita), (abhi, shrijit)}

    • {(shrijit, shraddha), (shraddha, shraddha), (shraddha, sanchita), (abhi, shrijit)}

CORRECT ANSWER : {(srijit, sanchita), (abhi, shraddha), (akash, sanchita), (srijit, shraddha)}

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

• 256

• 14

• 64

• 4096

CORRECT ANSWER: 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?

• 25

• 8

• 14

• 12

CORRECT ANSWER: 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?

• 𝑅 is reflexive and transitive

• 𝑅 is symmetric

• 𝑅 is anti-symmetric

• 𝑅 is reflexive but not transitive

CORRECT ANSWER: 𝑅 is reflexive and transitive

• 𝑅 is symmetric

• 𝑅 is anti-symmetric

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).

• 𝑅 is anti-symmetric

• 𝑅 is reflexive

• 𝑅 is transitive

• 𝑅 is symmetric

CORRECT ANSWER: 𝑅 is reflexive

• 𝑅 is transitive

• 𝑅 is symmetric

7. Which of the following is an equivalence relation?

• 𝑅 = {(𝑎,𝑏) | both 𝑎 and 𝑏 are even non-zero integers and a/b is an integer}

• 𝑅 = {(𝑥,𝑦) | 𝑦 − 𝑥 = 0}

• R={(1,2),(2,3),(3,4),(4,5),(5,6)}

• R={(𝑎,𝑏) | 𝑎 ≤ 𝑏³ }

CORRECT ANSWER: 𝑅 = {(𝑥,𝑦) | 𝑦 − 𝑥 = 0}

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?

• 7 and 128

• 12 and 144

• 12 and 4096

• 7 and 49

CORRECT ANSWER: 12 and 4096

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

• {1,2,3},{2,3,4,5}

• {4}{2}{3}{1,5}{2,3}

• {1,5},{2,3},{4,5}

• {1,2}{5}{3,4}

CORRECT ANSWER: {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?

• 9

• 3

• 6

• 12

CORRECT ANSWER: 9

WEEK-4 DETAILED SOLUTION