16. In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.
A =set of people who liked product A
B =set of people who liked product B
C =set of people who liked product C
n(A) =21
n(B)=26
n(C)=29
n( A intersection B )=14
n( B intersection C )=14
n( C intersection A )=12
n( A intersection B intersection C )=8
removing, n( A intersection B intersection C )=8
n( B intersection C and not A )=14-8 = 6
n( C intersection A and not B )=12-8 =4
We remove these two and also n( A intersection B intersection C )=8
to get
n(C) - n( B intersection C and not A ) - n( C intersection A and not B ) -n( A intersection B intersection C )
=29-6-4-8=11
therefore
11 people liked only product C
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chapter 1 miscellaneous sets ncert cbse
16. In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.
15. In a survey of 60 people, it was found that 25 people read newspaper
H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11
read both H and T, 8 read both T and I, 3 read all three newspapers.
Find:
(i) the number of people who read at least one of the newspapers.
(ii) the number of people who read exactly one newspaper
14. In a group of students, 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group?
13.
In a survey of 600 students in a school, 150 students were found to be
taking tea and 225 taking coffee, 100 were taking both tea and coffee.
Find how many
students were taking neither tea nor coffee?
11th cbse ncert chapter 2 relations and functions miscellaneous exercise
12. Let A = {9,10,11,12,13} and let f : A → N be defined by f (n) = the highest prime factor of n. Find the range of f.
11. Let f be the subset of Z × Z defined by f = {(ab, a + b) : a, b ∈ Z}. Is f a
function from Z to Z? Justify your answer.
10. Let A ={1,2,3,4}, B = {1,5,9,11,15,16} and f = {(1,5), (2,9), (3,1), (4,5), (2,11)}
Are the following true?
(i) f is a relation from A to B
(ii) f is a function from A to B.
Justify your answer in each case.
9. Let R be a relation from N to N defined by
R = {(a, b) : a, b ∈ N and a = (b^2) }.
Are the following true?
(i) (a,a) ∈ R, for all a ∈ N
(ii) (a,b) ∈ R, implies (b,a) ∈ R
(iii) (a,b) ∈ R, (b,c) ∈ R implies (a,c) ∈ R.
8. Let f = {(1,1), (2,3), (0,–1), (–1, –3)} be a function from Z to Z defined by
f(x) = ax + b, for some integers a, b. Determine a, b.
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