# Case study Chapter 1(Relation and Function)

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]

(i)Two neighbours X and Y ∈ I. X exercised his voting right while Y did not cast her vote in general election – 2019, while of the following is true ?

(a) (X, Y) ∈ R                        (b) (Y, X) ∈ R

(c) (X, X) ∉ R                         (d) (X, Y) ∉ R

(ii) Mr. ‘X’ and his wife ‘W’ both exercised their voting right in general election – 2019, which of the following is true ?

(a) Both (X, W) and (W, X) ∈ R                   (b) (X, W) ∈ R but (W, X) ∉ R

(c) Both (X, W) and (W, X) ∉ R                    (d) (W, X) ∈ R but (X, W) ∉ R

(iii) Three friends and exercised their voting right in general election- 2019, then which of the following is true

(a) and

(b) and

(c) but

(d) and

(iv) The above defined relation R is

(a) Symmetric and transitive but not reflexive

(b) Universal relation

(c) Equivalence relation

(d) Reflexive but not symmetric and transitive

(v) Mr. Shyam exercised his voting right in General Election – 2019, then Mr. Shyam is related to which of the following ?

(a) All those eligible voters who cast their votes

(b) Family members of Mr. Shyam

(c) All citizens of India

(d) Eligible voters of India

Solution: We have a relation ‘R’ is defined on I as follows:

and both use their voting right in general election -2019

Two neighbours  X and Y ∈ I. Simce X exercised his voting right while Y did not cast her vote in general election – 2019

Therefore, (X, Y) ∉ R

Since Mr. ‘X’ and his wife ‘W’ both exercised their voting right in general election -2019.

∴  Both (X, W) and (W, X) ∈ R

Since, three friends and exercised their voting right in general election – 2019, therefore

and

This relation is an equivalence relation.

Mr. Shyam exercised his voting right in General election – 2019, then Mr. Shyam is related to all tose eligible votes who cast their votes.

## Some other Case study problem

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.