# Case study Chapter 1 (Relation and Function)

Case study 2:- Sherlin and Danju are playing Ludo at home during COVID- 19. While rolling the dice, Sherlin’s sister Raji cbserved and noted the possible outcomes of the throw every time belongs to set {1, 2, 3, 4, 5, 6}. Let A be the set of players while B be the set of all possible outcomes.(Case study relation and function 2)

A = {S, D}, B = {1, 2, 3, 4, 5, 6}

Based on the above information answer the question.

(i) (a) Let R:B → B be defined by R = {(x, y) : y is divisible by x}. Verify that whether R is Reflexive, symmetric and transitive.

(b) Raji wnts to know the number of functions from A to B . Find the number of all possible functions.

(ii) (a) Let R be a relation on B defined by R = {(1, 2), (2, 2), (1, 3), (3, 4), (3, 1), (4, 3), (5, 5)}. Then R is which kind of relation ?

(b) Raji wants to know the number of relations possible from A to B. Find the number of possible relation.

Solution:(i) (a) Given R:B → B be defined by

R = {(x, y): y is divisible by x}

Reflexive: Let x ∈ B, Since x always divide x itself

⇒ (x, x) ∈ R

It is reflexive

Symmetric: Let 2, 6 ∈ B and let (2, 6) ∈ R

⇒  6 is divisible by 2.

⇒ 2 is not divisible by 6

⇒ (6, 2) ∉ R

It is not Symmetric.

Transitive: Let 1, 2, 6 ∈ B and

Since, (1, 2) ∈ R and (2, 6) ∈ R

⇒  2 is divisible by 1 and 6 is divisible by 2

⇒  6 is divisible by 1

⇒ (1, 6) ∈ R

It is transitive.

Hence, relation is reflexive and transitive but not symmetric.

(b) We have,

A = {S, D} ⇒ n(A) = 2

and B = {1, 2, 3, 4, 5, 6} ⇒ n(B) = 6

Number of functions from A to B is 6² = 36

(ii) (a) Given, R be a relation on B defined by

R = {(1, 2), (2, 2), (1, 3), (3, 4), (3, 1), (4, 3), (5, 5)}

R is not reflexive since (1, 1), (3, 3), (4, 4) ∉ R

R is not symmetric as (1, 2) ∈ R but (2, 1) ∉ R

And  R is not transitive as (1, 3) ∈ R and (3, 1) ∈ R but (1, 1) ∉ R

R is neither reflexive nor symmetric nor transitive.

(b) Total number of possible relations from A to B

Case study 1:- Read the following and answer the question:(Case study relation and function 1)

A general election of Lock sabha is a gigantic exercise. About 311 million people were eligible to vote and voter turnout  was about 67%, the highest ever

Let I be the set of all citizens of India who were eligible to exercise their voting right in general electio held in 2019. A relation ‘R’ is defined on I as follows:

and both use their voting right in general election – 2019]

Case Study 3:- Read the following and answer the question:(Case study relation and function 3)

An organization conducted bike race under 2 different categories- boys and girls. In all, there were 250 participants. Among all of them finally three from category 1 and two from category 2 were selected for the final race. Ravi from two sets B and G with these participants for his college project.

Let and where B represents the set of boys selected and G the set of girls who were selected for the final race.

Ravi decides to explore these sets for various types of relations and functions