Mathematics for Data Science I Quiz 1: 16 July 2023 (May 2023 term)

Let $S = \{\text{Jan, Feb, March, April, May}\}$ be a set of months of a particular year. Consider the following relations on the set $S$.

• $R_1 = \{\text{ (Feb, Feb), (March, April), (April, March), (March, March) }\}$
• $R_2 = \{\text{ (Jan, Jan), (Feb, Feb), (March, March), (April, April), (May, May) }\}$

From the below list of given terms find out the best possible options for each of the given subquestions:

1. Reflexive relation
2. Symmetric relation
3. Transitive relation
4. Not a equivalence relation
5. Not a function
6. Injective (One-one) function
7. Surjective (Onto) Function

R1 is _____________ . (Enter all correct options. Enter only the serial numbers of those options in increasing order without adding any comma or space in between them i.e., if your answer is 6 and 7, then you should enter 67]

Let $S = \{\text{Jan, Feb, March, April, May}\}$ be a set of months of a particular year. Consider the following relations on the set $S$.

• $R_1 = \{\text{ (Feb, Feb), (March, April), (April, March), (March, March) }\}$
• $R_2 = \{\text{ (Jan, Jan), (Feb, Feb), (March, March), (April, April), (May, May) }\}$

From the below list of given terms find out the best possible options for each of the given subquestions:

1. Reflexive relation
2. Symmetric relation
3. Transitive relation
4. Not a equivalence relation
5. Not a function
6. Injective (One-one) function
7. Surjective (Onto) Function

R2 is ____________ . (Enter all correct options. Enter only the serial numbers of those options in increasing order without adding any comma or space in between them i.e., if your answer is 3 and 4, then you should enter 34)

Let $S = \{\text{Jan, Feb, March, April, May}\}$ be a set of months of a particular year. Consider the following relations on the set $S$.

• $R_1 = \{\text{ (Feb, Feb), (March, April), (April, March), (March, March) }\}$
• $R_2 = \{\text{ (Jan, Jan), (Feb, Feb), (March, March), (April, April), (May, May) }\}$

From the below list of given terms find out the best possible options for each of the given subquestions:

1. Reflexive relation
2. Symmetric relation
3. Transitive relation
4. Not a equivalence relation
5. Not a function
6. Injective (One-one) function
7. Surjective (Onto) Function

Find the cardinality of the set (S × S) \ R2.