# 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)

Â A = {S, D}, B = {1, 2, 3, 4, 5, 6}

Based on the above information answer the question.

(i) (a) Let R:B â†’ 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 â†’ B be defined by

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

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

â‡’ (x, x) âˆˆ R

It is reflexive

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

â‡’Â  6 is divisible by 2.

â‡’ 2 is not divisible by 6

â‡’ (6, 2) âˆ‰ R

It is not Symmetric.

Transitive: Let 1, 2, 6 âˆˆ B and

Since, (1, 2) âˆˆ R and (2, 6) âˆˆ R

â‡’Â  2 is divisible by 1 and 6 is divisible by 2

â‡’Â  6 is divisible by 1

â‡’ (1, 6) âˆˆ R

It is transitive.

Hence, relation is reflexive and transitive but not symmetric.

(b) We have,

A = {S, D} â‡’ n(A) = 2

and B = {1, 2, 3, 4, 5, 6} â‡’ n(B) = 6

Number of functions from A to B is 6Â² = 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) âˆ‰ R

R is not symmetric as (1, 2) âˆˆ R but (2, 1) âˆ‰ R

AndÂ  R is not transitive as (1, 3) âˆˆ R and (3, 1) âˆˆ R but (1, 1) âˆ‰ 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 turnoutÂ  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)

Â 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

Case study 4:- Read the following answer the question(Case study relation and function 4)

Â  Student of gade 9,planned to plant saplings along straight lines, parallel to each other to one side of the play ground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x – 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.