SETS :Practice set 1.4
Question 1:
If n (A) = 15, n (A∪B ) = 29, n (A ∩ B) = 7 then n (B) = ?
ANSWER:
n (A) = 15, n (A∪B ) = 29, n (A ∩ B) = 7
Since, n (B) = n (A∪B ) + n (A ∩ B) − n (A) = 29 + 7 - 15
So, n (B) = 21
Question 2:
In
a hostel there are 125 students, out of which 80 drink tea, 60 drink coffee and
20 drink tea and coffee both. Find the number of students who do not drink tea
or coffee.
ANSWER:
Let A be the set of students who drink tea, and B be the
set of students who drink coffee.
We have,
n(U) = 125, n(A) = 80, n(B) = 60, n (A∩B) = 20n (A∩B) = 20
Since,
n(A∪B) = n(A) + n(B) - n(A∩B) = 80 + 60 - 20
(A∪B) = 120
So, the number of students who do not drink tea or coffee = 125 - 120 = 5
Question 3:
In
a competitive exam 50 students passed in English. 60 students passed in
Mathematics. 40 students passed in both the subjects. None of them fail in both
the subjects. Find the number of students who passed at least in one of the
subjects ?
ANSWER:
Let A be the set of students who passed in English, and B be the set of students who passed in Mathematics.
We have,
n(A) = 50, n(B) =60, n (A∩B) = 40
Since,
n (A∪B) = n(A) + n(B) − n(A∩B) = 50 + 60 −40
n (A∪B) = 70
So, the number of students who passed at least in one of the subjects is
70.
Question 4:
A
survey was conducted to know the hobby of 220 students of class IX. Out of
which 130 students informed about their hobby as rock climbing and 180 students
informed about their hobby as sky watching. There are 110 students who follow
both the hobbies. Then how many students do not have any of the two hobbies ?
How many of them follow the hobby of rock climbing only ? How many students
follow the hobby of sky watching only ?
ANSWER:
Let A be the set of students who follow the hobby of rock
climbing, and B be the set of students who follow the hobby of sky watching.
We have, n (A) = 130, n (B) = 180, n (A ∩ B) = 110, n (U) =
220
Since,
n (A ∪ B) = n (A) + n (B) − n (A ∩ B) = 130 + 180 − 110 = 200
So, the number of students who do not have any of the two hobbies = n
(U) − n (A ∪ B) = 220 − 200 = 20
Also, the number of students who follow the hobby of rock climbing only
= n (A) − n (A ∩ B) = 130 − 110 = 20
And, the number of students who follow the hobby of sky watching only
= n (B) − n (A ∩ B) = 180 − 110 = 50
Question 5:
Observe the given Venn diagram
and write the following sets.
(i)
A (ii) B (iii) A∪B (iv) U
(v) A' (vi) B' (vii) (A∪B) '
ANSWER:
We
have,
(i)
A = {m, n, x, y, z}
(ii) B = {m, n, p, q, r}
(iii) A∪B = {m, n, x, y,
z, p, q, r}
(iv) U = {m, n, x, s, t, y, z,
p, q, r}
(v) A' = {m, n, s, t, p, q, r}
(vi) B' = {m, n, x, s, t, y, z}
(vii) (A∪B)' = {s, t}