Chapter – 2
Relations & Functions
Class
XI » [Module : 2.1]
Que
1.
Which of the following are sets? Justify your answer.
(i) The collection of
all months of a year beginning with the letter J.
(ii) The collection of
ten most talented writers of India.
(iii) A team of eleven
best-cricket batsmen of the world.
(iv) The collection of
all boys in your class.
(v) The collection of
all natural numbers less than 100.
Que
2.
Write the following sets in the set-builder form:
(i) (3, 6, 9, 12) (ii) {2, 4, 8, 16, 32} (iii) {5, 25, 125, 625} (iv) {2, 4, 6 …}
Que
3.
List all the elements of the following sets:
(i) A = {x: x is an odd
natural number} (ii) B = {x: x
is an integer,}
(iii) C = {x: x is an
integer, (iv)
D = {x: x is a letter in the word “LOYAL”}
(v) E = {x: x is a
month of a year not having 31 days}
(vi) F = {x: x is a
consonant in the English alphabet which proceeds k}.
Que
4.
Which of the following are examples of the null set:
(i) Set of odd natural numbers divisible by 2
(ii)
Set of even prime numbers
(iii) {x:x is a natural numbers, x < 5 and x > 7 }
(iv)
{y:y is a point common to any two parallel lines}
Que
5.
Which of the following sets are finite or infinite
(i) The set of months of a year
(ii) {1, 2, 3 ...}
(iii) {1, 2, 3 ... 99, 100}
(iv) The set of positive integers greater than 100
(v) The set of prime numbers less
than 99
Que
6.
Which of the following sets are finite or infinite
(i) The set of months
of a year (ii) {1, 2,
3 ...} (iii) {1, 2, 3 ...
99, 100}
(iv) The set of
positive integers greater than 100 (v) The set of prime numbers less
than 99
Que
7.
In the following, state whether A = B or not:
(i) A = {a, b, c, d}; B
= {d, c, b, a} (ii) A = {4, 8, 12, 16}; B
= {8, 4, 16, 18}
(iii) A = {2, 4, 6, 8,
10}; B = {x: x is positive even integer and x ≤ 10}
(iv) A = {x: x is a
multiple of 10}; B = {10, 15, 20, 25, 30 ...}
Que
8.
Are the following pair of sets equal? Give reasons.
(i) A = {2, 3}; B = {x:
x is solution of x2 + 5x + 6 = 0}
(ii) A = {x: x is a
letter in the word FOLLOW}; B = {y: y is a letter in the word WOLF}
Que
9.
From the sets given below, select equal sets: A = {2, 4, 8, 12}, B = {1, 2, 3, 4}, C = {4,
8, 12, 14}, D = {3, 1, 4, 2} E = {–1, 1}, F = {0, a}, G = {1, –1}, H = {0, 1}
Que 10.
Let A= {1, 2, {3, 4,}, 5}. Which of the following statements are incorrect and
why?
(i)
{3, 4}⊂ A
(ii)
{3, 4}}∈ A
(iii)
{{3, 4}}⊂ A
(iv)
1∈ A
(v)
1⊂ A
(vi)
{1, 2, 5} ⊂
A
(vii)
{1, 2, 5} ∈
A 3
(viii)
{1, 2, 3} ⊂
A
(ix)
Φ ∈ A (x) Φ ⊂ A
(xi)
{Φ} ⊂ A
Que 11.
How many elements has P(A), if A = Φ?
Que
12.
What universal set (s) would you propose for each of the following?
(i) The set of right triangles
(ii)
The set of isosceles triangles
Que 13.
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10};
find:(i) A ∪
B
(ii)
A UC
(iii)
B ∪ C
(iv)
B ∪ D
(v)
A ∪ B ∪ C
(vi)
A ∪ B ∪ D
(vii) B ∪
C ∪ D
Que 14. If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find:(i) A ∩ B
(ii)
B ∩ C
(iii)
A ∩ C ∩ D
(iv)
A ∩ C
(v)
B ∩ D
(vi)
A ∩ (B U C)
(vii)
A ∩ D
(viii)A
∩ (B U D)
(ix)
(A ∩ B) ∩ (B UC)
(x) (A UD) ∩ (B UC)
Que 15.
If A = {x: x is a natural number}, B ={x: x is an even natural number} C = {x:
x is an odd natural number} and D = {x: x is a prime number}:
find (i) A ∩ B (ii) A ∩
C (iii) A ∩ D (iv) B ∩ C (v) B ∩ D (vi) C ∩ D
Que 16.
Which of the following pairs of sets are disjoint
(i)
{1, 2, 3, 4} and {x: x is a natural number and 4 ≤ x ≤ 6}
(ii) {a, e, i, o, u} and {c, d, e, f}
(iii)
{x: x is an even integer} and {x: x is an odd integer}
Que 17.
If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10,
12, 14, 16}, D = {5, 10, 15, 20}; find
(i)
A – B
(ii)
A – C
(iii)
A – D
(iv)
B – A
(v)
C – A
(vi)
D – A
(vii)
B – C
(viii)
B – D
(ix)
C – B
(x)
D – B
(xi)
C – D
(xii)
D – C
Que 18.
If X = {a, b, c, d} and Y = {f, b, d, g}, find (i) X – Y (ii) Y – X (iii) X ∩ Y
Que
19.
If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:
(i) A = {a, b, c} (ii) B = {d, e, f, g} (iii) C = {a, c, e, g} (iv) D = {f, g,
h, a}
Que 20. Taking the set of natural numbers as the universal set, write down the complements of the following sets:
(i) {x: x is an even natural number}
(ii) {x: x is an odd natural number}
(iii) {x: x is a positive multiple of 3}
(iv) {x: x is a prime number}
(v) {x: x is a natural number divisible by 3 and 5}
(vi) {x: x is a perfect square}
(vii) {x: x is perfect cube}
Sets » [Module : 1.3]
1. If n (A) = 33, n (B) = 27 and n (AUB) = 58, find n (AB).
2. A and B are two sets such that n (A) = 27, n (B) = 33 and n (AB) =
15. Find n (AUB).
3. If n (AUB) = 60, n (AB)= 10 and n (A) = 40, find n (B).
4. If n (A) = 300, n (B) = 200 and n (A U B) = 400. Find n (A – B) and n
(B – A).
5. A and B are two sets such that n (A – B)=15, n (AB) = 10 and n (B – A)
25. Find n (AUB),
6. n (A) and n (B). 6. There are 240 students in class XI in a school
who study Mathematics or Physics. Of these, 80 study Physics and 20 study both
Mathematics and Physics. How many study Mathematics?
7. In a group of 500 persons, 350 can speak Hindi, 250 can speak English
and 150 can speak both Hindi and English. Find the number of persons who can
speak neither Hindi nor English.
8. (a) In a group of 1000 persons, 700 can speak Hindi and 500 can speak
English. If every person can speak atleat one of the two languages Hindi and
English, find the number of persons who can speak (f) both Hindi and English
(i) Hindi only (iii) English only.
(b) In a class of 35 students, 24 like to play cricket and 16 like to
play football. Also, each student likes to play atleast one of the two games.
How many students like to play both cricket and football?
9. In a group of 150 persons, 70 read English newspaper, 90 read Hindi
newspaper and 40 read both the newspapers. How many persons read (f) English
newspaper only? (i) Hindi newspaper only ? (iii) neither English nor Hindi
newspaper?
10. (a) In a group of 100 persons, 60 like bananas, 75 like apples. If x
persons like both Bananas and apples. show that 35 x560, (b) A survey shows
that 66% of Indians like cheese and 74% of them like fruits and x% like both.
Show that 40 x 66.
11. Of the members of three sports teams in a certain school 23 are in
the Cricket team, 27 in the Hockey team and 30 in the Football team. 15 play
both Hockey and Cricket, 16 play both Hockey and Football, 14 play Football and
Cricket and 9 play all the three games. Find the total number of members of the
three teams.
12. In a class of 50 students, 27 study History, 27 study Civics, 16 study
both Civics and Economics 14 study both History and Economics, 25 study
Economics, 9 study all the three subjects and 15 study both History and Civics.
How many students do not study any of the three subjects?
13. In a survey of 100 students, the number of
students studying the various languages were found to be as
follows:
English only
18 /
English but not Hindi 23 /
English and Panjabi 8 /
Panjabi 48 Panjabi and Hindi 8 /
No language 24 / English 26
Find (i) How many students were studying Hindi?
(ii) How many students were studying English and
Hindi?
14. (a) In a survey of 100 persons it was found that 28 read magzine A,
30 read magzine B, 42 read magzine C, 9 read magzines A and B. 11 read magzines
A and C, 6 read magzines B and C and 4 read all the three magzines. Find (i) How many read none of the three magzines?
(ii) How many read magzine C only ?
(b) In a town of 10,000 families it was found that 40% families buy newspaper A. 20% families buy newspaper B. 10% families buy newspaper C, 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% buy all the three newspapers, find (i) the number of families who buy newspaper A only. (ii) the number of families who buy none of A, B and C.
15. In a group of 50 students, the number of students playing Hockey, Cocket and Football were found to be as follows:
Cricket 17 / Football and Hockey 4 / Football 13 Hockey and Cricket 5 / Hockey 15 / Hockey, Cricket and Football 3 / Cricket and Football 9
Find the number of students who play
(i) Cricket only
(ii) Football only
(iii) Cricket and Football but not Hockey
(iv)Hockey only
(v) Football and Hockey but not Cricket
(vi) Hockey and Cricket but not Football
(vii) atleast one of the three games
16. In a survey of 200 students of a school, it was found that 120 study Mathematics, 90 study Physics, 70 study Chemistry, 40 study Mathematics and Physics, 30 study Physics and Chemistry, 50 study Chemistry and Mathematics and 20 study none of the three subjects. Find the number of students who study all the three subjects.
17. Out of 500 car owners investigated, 400 owned the car A and 200
owned the car B. 50 owned both the cars A and B. Is this data correct 7
