Mathematics Assignment
Class - XI | Subject Mathematics | Chapter - 1
Math Assignment Class XI Chapter 1 Set Theory, Extra and important questions on Set Theory useful for Mat and Applied Math students.
MATHEMATICS ASSIGNMENT
SET THEORY
For Non-Medical /Applied Math Students
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Q1
Write the following sets in tabular form
a){ x :
x = 2n + 1 ; n ∈ N} Ans{3, 5, 7, 9, ........}
b) {x :
x – 1 = 0} Ans {1}
c) {x :
x = prime number and x ≤ 7 ; x ∈ N
Ans { 2, 3, 5, 7}
d) {x :
x ∈
I,
3x - 2 = 3} Ans {φ}
e) {x :
x2 ≤ 10 , x ∈ Z } Ans{0, 土1, 土2, 土3}
Q 2
Write the following in set builder form
a)
{10, 11, 12, 13, 14, 15} Ans {x : x ∈ N : 9 < x < 16
b) 1, 4,
9, .........., 121} Ans {x2 : x
∈ N ; 1
≤ x ≤ 10
Q3
Write the subsets of the set A = {1, 2, {3}}
Ans
φ, {1}, {2}, {{3}}, {1,2}, {1, {3}}, {2, {3}}, {1, 2, {3}}
Q4
Write the proper subsets of A = {5, 10, 11, 15}
Ans: Except { 5, 10, 11, 15}, all other subsets of A are proper subsets.
Q5
Write the power set of A = { φ, 1}
Ans: P(A) = {φ, {φ}, {1}, { φ, 1}}
Q6
List all the subsets of set {-1, 0, 1}
Ans φ,
{-1}, {0}, {1}, {-1, 0}, {0, 1}, {-1, 1}, {-1, 0, 1}
Q7
From the sets given below select the equal and equivalent sets
A =
{0, 1, 2}, B = {a, b}, C = {1, 0, 2},
D = {3, 5, 9, 13} E = {5,
25}, F = {1, d}
Ans
Equal sets: A and C,
Equivalent Sets : B, E and F ; A and C
Q8 Let
S = {x: x is a positive multiple of 3, less than 100}
P= {x :
x is a prime number less than 20}
then
find n(S) + n(P) Ans 41
Q 9
Let A and B are two sets , show A - B , A ∩ B, B - A in venn diagram.
Q 10
If A = {a, b, c, d. e}, B = {a, c, e, g}, C = {b, e, f, g} verify that
(a)
A ∩ (B - C) = (A ∩ B) - (A ∩ C)
(b) A -
(B ∩ C) = (A - B) ⋃ (A - C)
Q11 If
A , B and C are two sets then, prove that
a)
A ⋃(A ∩ B) = A
b) (A ⋃ B) – B = A - B
c) (A - B) ⋃ (A ∩ B = A
d) A ⋃ (B - A) = A ⋃ B
e) A -
(A ∩ B) = A - B
f) A ⋃ B) – B = A -
B
Q 12
If A = {1, 2, 3, 4, 5}, B = {1, 3, 5, 7,
9}, C = {2, 3, 4}, verify that
A - (B
⋃ C) = (A - B)
∩ (A - C)
Following questions are deleted from CBSE syllabus
Q 13
In a class of 35 students, 24 like to play cricket and 16 like to play
football. Also each student like to play at least one of the two games. How
many like to play both Cricket and Football. Ans 5
Q
14 In a survey of 400 students in the school, 100 were taking apple
juice, 150 were taking orange juice. Find how many students were taking neither
apple juice not orange juice. Ans 225
Q 15 A college awarded 38 medals in football, 15 in basketball and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports ? Ans 9
Q 16
In a group of 200 students, it was found that 120 study maths, 90 study
Physics, 70 study Chemistry, 40 study Maths and Physics, 30 study Physics and
Chemistry, 50 study Chemistry and Maths, 20 study all the three subject.
Find the number of students.
(i)
Who study all the three subjects ? Ans 20
(ii)
Who study maths only ? Ans a = 50
(iii)
Who study one of the three subject ? Ans 100
(iv)
Who study two of the three subjects ? Ans 60
Q 17
Out of 100 students, 15 passed in english, 12 passed in Maths, 8 passed in science,
6 in English and Maths, 7 in Maths and Science, 4 in English and science, 4 in
all three. Find how many passed in
(i)
English and Maths but not in science Ans 2
(ii)
Maths and Science but not in English Ans 3
(iii)
Maths only. Ans 3
(iv)
More than one subject only Ans 9
Q 18
In a group of 50 students , 17 students studying French , 13 English, 15
Sanskrit, 9 studying French and English, 4 Studying English and Sanskrit, 5
studying French and Sanskrit, 3 studying all the three subjects. Find the
number of students who study.
(i)
Only French, Ans 6
(ii)
Only English Ans 3
(iii)
Only Sanskrit Ans 9
(iv)
English and Sanskrit but not French Ans 1
v)
French and Sanskrit but not English Ans 2
(vi)
French and English but not Sanskrit Ans 6
(Vii)
At least one of the three languages And 30
(viii)
None of the three languages Ans 20
Q 19 In a group of 100 people
65 like to play Cricket, 40 like to play Tennis and 55 like to play Volleyball.
All of them like to play at least one of three games. If 25 like to play Both
Cricket and Tennis 24 like to play both Tennis and Volleyball and 22 like to
play Both Cricket and Volleyball then
a) How many like to play all three games?
b) How many like to play Cricket only?
c) How many like to play Tennis only?
Solution Hint:
C∩T = a + b = 25T∩V = a + d = 24
C∩V = a + c = 22
P(C⋃T⋃V) = n(C) + n(T) + n(V) - n(C∩T) - n(T∩V) - n(V∩T + n(C∩T∩V)
100 = 65 + 40 + 55 - 25 - 24 - 22 + a
100 = 89 + a
11 = a
b = 25 - 11 = 14
d = 24 - 11 = 13
c = 22 - 11 = 11
n(Cricket only) = 65 - a - b - c = 65 - 11 - 14 - 11 = 29
n(Tennis only) = 40 - a - b - d = 40 - 11 - 14 - 13 = 2
n(Volleyball only) = 55 - a - c - d = 55 - 11 - 11 - 13
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