**Case study Chapter 1 (Relation and Function)**

**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**

**(i) Ravi wishes to form all the relations possible from B to G. How many such relations are possible ?**

(a) (b)

(c) 0 (d)

**(ii) Let R:B → B be defined by R = {(x, y): x and y are students of same sex}, Then this relation R is**

(a) Equivalence (b) Reflexive only

(c) Reflexive and symmetric but not transitive

(d) Reflexive and transitive but not symmetric

**(iii) Ravi wants to know among those relation, how many functions can be formed from B to G ?**

(a) (b)

(c) (d)

**(iv) Let R:B → G be defined by** then R is

(a) Injective (b) Surjective

(c) Neither Surjective nor Injective

(d) Surjective and Injective

**(v) Ravi find the number of injective function B to G. How many numbers of injective function are possible ?**

(a) 0 (b) 2!

(c) 3! (d) 0!

**Solution: We have sets**

and

⇒ n(A) = 3and n(B) = 2

**(i) Answer (a)**

Number of all possible relation from B to G =

**(ii) Answer (a)**

Given relation R = {(x, y): x and y are students of same sex}

On the set B.

Since the set is = all boys

∴ It is an equivalence relation

**(iii) Answer (d)**

We have

and

⇒ n(A) = 3and n(B) = 2

Total number of possible function from B to G = 2³

**(iv) Answer (b)**

R:B → G be defined by

It is not injective because and

So ⇒ same image .

It is surjective because its co-domain = range.

∴ R is surjective.

**(v) Answer (a)**

Since n(B) = 3, n(G) = 2

∴ Number of one -one functions from B to A = 0

## Some other case study problem

**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]

**Solution:** For solution click here

**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.**

**Solution:** For solution click here

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

** 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.**

**Solution:** For solution click here