Sets
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47. In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?
47. In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?
47. Let C and T be the set of people who likes cricket and tennis respectively. Then,
n (C) = 40, people who likes cricket
n (C T) = 65, people who likes either cricket or tennis
and n (C T) = 10, people who likes both
So, n (C T) = n (C) + n (T) n (C T)
65 = 40 + n (T) 10
n (T)
Upvote 
46. In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?
46. In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?
46. Let A and B but the set of people who likes coffee and tea.
Then, n (A) = 37. no. of people who like coffee
n (B) = 52, no. of people who like tea.
As each person likes at least one of the two drink,
n (A B) = 70.
So using, n (A B) = n (A) + n (B) n (A B)
n (A B) = n (A) + n
Upvote 45. If X and Y are two sets such that X has 40 elements, X Y has 60 elements and X Y has 10 elements, how many elements does Y have?
45. If X and Y are two sets such that X has 40 elements, X Y has 60 elements and X Y has 10 elements, how many elements does Y have?
45. Given, n (X) = 40
n (Y Y) = 60.
n (X Y) = 10.
n (Y) =?
Using, n (X Y) = n (X) + n (Y) n (X Y)
60 = 40 + n (y) 10.
n (Y) = 60 - 40 + 10
n (Y) = 30.
Upvote 44. If S and T are two sets such that S has 21 elements, T has 32 elements, and S ∩T has 11 elements, how many elements does S T have?
44. If S and T are two sets such that S has 21 elements, T has 32 elements, and S ∩T has 11 elements, how many elements does S T have?
44. Given, n (S) = 21
n (T) = 32
n (S T) = 11.
Using, n (S T) = n (S) + n (T) n (S T)
= 21 + 32 11
= 42.
Upvote 43. In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?
43. In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?
43. Let H and E be set if people who speak Hindi and English respectively. there,
n (H) = 250, people speak Hindi n (E) = 200, people speak English
n (H E) = 400, people speaks either Hindi or English
So, n (H E) = n (H) + n (E) n (H E)
= 250 + 200 400
= 50
So, 50 people can speak bo
Upvote 42. If X and Y are two sets such that X Y has 18 elements, X has 8 elements and Y has 15 elements; how many elements does X Y have?
42. If X and Y are two sets such that X Y has 18 elements, X has 8 elements and Y has 15 elements; how many elements does X Y have?
42. Given, n (X Y) = 18.
n (X) = 8.n (Y) = 15.n (X Y) =?
Using n (X Y) = n (X) + n (Y) n (X Y)
= 8 + 15 18.
= 5.
Upvote Class 11 Sets Exercise 1.6 Solutions
41. If X and Y are two sets such that n( X ) = 17, n ( Y ) = 23 and n(X Y) = 38, find n(X Y).
Class 11 Sets Exercise 1.6 Solutions
41. If X and Y are two sets such that n( X ) = 17, n ( Y ) = 23 and n(X Y) = 38, find n(X Y).
41. Given, n (X)= 17
n (Y) = 23
n (X Y)= 38.
So, n (X Y) = n (X) + n (Y) n (X Y)
n (X Y) = n (X) + n (Y) n (X Y)
= 17 + 23 38.
= 2
Upvote 40. Fill in the blanks to make each of the following a true statement :
(i) A A= . . .
(ii) A = . . .
(iii) A A= . . .
(iv)U A = . . .
40. Fill in the blanks to make each of the following a true statement :
(i) A A= . . .
(ii) A = . . .
(iii) A A= . . .
(iv)U A = . . .
40. (i) A A = U
(ii) ∩ A = U ∩ A = A.
(iii) A ∩ A = .
(iv) U ∩ A = ∩ A = .
Upvote 39. Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A?
39. Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A?
39. A = U – A
= Set of all triangle in a plane - Set of all triangle with at least the angle different from 60°.
= Set of all triangle with each angle 60°.
A? = set of all equilateral triangle.
Upvote 38. Draw appropriate Venn diagram for each of the following :
(i) (A B) , (ii) A B , (iii) (A B) , (iv) A B
38. Draw appropriate Venn diagram for each of the following :
(i) (A B) , (ii) A B , (iii) (A B) , (iv) A B
38. (i) (A B) = U – (A B)
(ii) A ∩ B = (AU B) = U – (AU B)
Upvote