Relation and Function
CASE STUDY 1:
A general election of Lok Sabha is a gigantic exercise. About 911 million people were
eligible to vote and voter turnout was about 67%, the highest ever
ONE – NATION
ONE – ELECTION
FESTIVAL OF
DEMOCRACY
GENERAL ELECTION –
2019
Let I be the set of all citizens of India who were eligible to exercise their voting right in
general election held in 2019. A relation ‘R’ is defined on I as follows:
R = {(𝑉1, 𝑉2) ∶ 𝑉1, 𝑉2 ∈ 𝐼 and both use their voting right in general election – 2019}
1. Two neighbors X and Y∈ I. X exercised his voting right while Y did not cast her vote
in general election – 2019. Which of the following is true?
a. (X,Y) ∈R
b. (Y,X) ∈R
c. (X,X) ∉R
d. (X,Y) ∉R
2. 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
3. Three friends F1, F2 and F3 exercised their voting right in general election-2019, then
which of the following is true?
a. (F1,F2 ) ∈R, (F2,F3) ∈ R and (F1,F3) ∈ R
b. (F1,F2 ) ∈ R, (F2,F3) ∈ R and (F1,F3) ∉ R
c. (F1,F2 ) ∈ R, (F2,F2) ∈R but (F3,F3) ∉ R
d. (F1,F2 ) ∉ R, (F2,F3) ∉ R and (F1,F3) ∉ R
, 4. 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
5. 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
ANSWERS
1. (d) (X,Y) ∉R
2. (a) both (X,W) and (W,X) ∈ R
3. (a) (F1,F2 ) ∈R, (F2,F3) ∈ R and (F1,F3) ∈ R
4. (c) Equivalence relation
5. (a) All those eligible voters who cast their votes
CASE STUDY 2
Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice,
Sherlin’s sister Raji observed 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.
A = {S, D}, B = {1,2,3,4,5,6}
,1. Let 𝑅 ∶ 𝐵 → 𝐵 be defined by R = {(𝑥, 𝑦): 𝑦 𝑖𝑠 𝑑𝑖𝑣𝑖𝑠𝑖𝑏𝑙𝑒 𝑏𝑦 𝑥 } is
a. Reflexive and transitive but not symmetric
b. Reflexive and symmetric and not transitive
c. Not reflexive but symmetric and transitive
d. Equivalence
2. Raji wants to know the number of functions from A to B. How many number of
functions are possible?
a. 62
b. 26
c. 6!
d. 212
3. 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
a. Symmetric
b. Reflexive
c. Transitive
d. None of these three
4. Raji wants to know the number of relations possible from A to B. How many
numbers of relations are possible?
a. 62
b. 26
c. 6!
d. 212
5. Let 𝑅: 𝐵 → 𝐵 be defined by R={(1,1),(1,2), (2,2), (3,3), (4,4), (5,5),(6,6)}, then R is
a. Symmetric
b. Reflexive and Transitive
c. Transitive and symmetric
d. Equivalence
ANSWERS
1. (a) Reflexive and transitive but not symmetric
2. (a) 62
3. (d) None of these three
4. (d) 212
5. (b) Reflexive and Transitive
, CASE STUDY 3:
An organization conducted bike race under 2 different categories-boys and girls. Totally
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 forms two sets B and G with these
participants for his college project.
Let B = {b1,b2,b3} G={g1,g2} 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
1. Ravi wishes to form all the relations possible from B to G. How many such relations
are possible?
a. 26
b. 25
c. 0
d. 23
2. 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
3. Ravi wants to know among those relations, how many functions can be formed
from B to G?
a. 22
b. 212
c. 32
d. 23
4. Let 𝑅: 𝐵 → 𝐺 be defined by R = { (b1,g1), (b2,g2),(b3,g1)}, then R is__________
CASE STUDY 1:
A general election of Lok Sabha is a gigantic exercise. About 911 million people were
eligible to vote and voter turnout was about 67%, the highest ever
ONE – NATION
ONE – ELECTION
FESTIVAL OF
DEMOCRACY
GENERAL ELECTION –
2019
Let I be the set of all citizens of India who were eligible to exercise their voting right in
general election held in 2019. A relation ‘R’ is defined on I as follows:
R = {(𝑉1, 𝑉2) ∶ 𝑉1, 𝑉2 ∈ 𝐼 and both use their voting right in general election – 2019}
1. Two neighbors X and Y∈ I. X exercised his voting right while Y did not cast her vote
in general election – 2019. Which of the following is true?
a. (X,Y) ∈R
b. (Y,X) ∈R
c. (X,X) ∉R
d. (X,Y) ∉R
2. 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
3. Three friends F1, F2 and F3 exercised their voting right in general election-2019, then
which of the following is true?
a. (F1,F2 ) ∈R, (F2,F3) ∈ R and (F1,F3) ∈ R
b. (F1,F2 ) ∈ R, (F2,F3) ∈ R and (F1,F3) ∉ R
c. (F1,F2 ) ∈ R, (F2,F2) ∈R but (F3,F3) ∉ R
d. (F1,F2 ) ∉ R, (F2,F3) ∉ R and (F1,F3) ∉ R
, 4. 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
5. 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
ANSWERS
1. (d) (X,Y) ∉R
2. (a) both (X,W) and (W,X) ∈ R
3. (a) (F1,F2 ) ∈R, (F2,F3) ∈ R and (F1,F3) ∈ R
4. (c) Equivalence relation
5. (a) All those eligible voters who cast their votes
CASE STUDY 2
Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice,
Sherlin’s sister Raji observed 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.
A = {S, D}, B = {1,2,3,4,5,6}
,1. Let 𝑅 ∶ 𝐵 → 𝐵 be defined by R = {(𝑥, 𝑦): 𝑦 𝑖𝑠 𝑑𝑖𝑣𝑖𝑠𝑖𝑏𝑙𝑒 𝑏𝑦 𝑥 } is
a. Reflexive and transitive but not symmetric
b. Reflexive and symmetric and not transitive
c. Not reflexive but symmetric and transitive
d. Equivalence
2. Raji wants to know the number of functions from A to B. How many number of
functions are possible?
a. 62
b. 26
c. 6!
d. 212
3. 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
a. Symmetric
b. Reflexive
c. Transitive
d. None of these three
4. Raji wants to know the number of relations possible from A to B. How many
numbers of relations are possible?
a. 62
b. 26
c. 6!
d. 212
5. Let 𝑅: 𝐵 → 𝐵 be defined by R={(1,1),(1,2), (2,2), (3,3), (4,4), (5,5),(6,6)}, then R is
a. Symmetric
b. Reflexive and Transitive
c. Transitive and symmetric
d. Equivalence
ANSWERS
1. (a) Reflexive and transitive but not symmetric
2. (a) 62
3. (d) None of these three
4. (d) 212
5. (b) Reflexive and Transitive
, CASE STUDY 3:
An organization conducted bike race under 2 different categories-boys and girls. Totally
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 forms two sets B and G with these
participants for his college project.
Let B = {b1,b2,b3} G={g1,g2} 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
1. Ravi wishes to form all the relations possible from B to G. How many such relations
are possible?
a. 26
b. 25
c. 0
d. 23
2. 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
3. Ravi wants to know among those relations, how many functions can be formed
from B to G?
a. 22
b. 212
c. 32
d. 23
4. Let 𝑅: 𝐵 → 𝐺 be defined by R = { (b1,g1), (b2,g2),(b3,g1)}, then R is__________
