Sets and Functions
- Let A = {x: x ∈ N ∧ x is a multiple of 2};
B = {x: x ∈ N ∧ x is a multiple of 5};
C = {x: x ∈ N ∧ x is a multiple of 10};
Describe the set (A ∩ B) ∩ C,
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A = {2, 4, 6,…........}
B = {5, 10, 15,…...}
C = {10, 20, 30,….}Correct Option: D
A = {2, 4, 6,…}
B = {5, 10, 15,…}
C = {10, 20, 30,…}
∴ (A ∩ B) = {2, 4, 6…} ∩ {5, 10, 15,…} = {10, 20, 30,…} = C
∴ (A ∩ B) ∩ C = C ∩ C = C.
- There were 600 students in a school. Each offered either English or Hindi or Both . If 75% offered English and 45% Hindi, how many offered both ?
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n(A) = 75% of 600 = 450
n(B) = 45% of 600 = 270 and n(A ∪ B) = 600
∵ n(A∩B) = n (A) + n(B) - n(A∪B) = (450 + 270 - 600) = 120Correct Option: D
n(A) = 75% of 600 = 450
n(B) = 45% of 600 = 270 and n(A ∪ B) = 600
∵ n(A∩B) = n (A) + n(B) - n(A∪B) = (450 + 270 - 600) = 120
- Which of the following pairs of sets are not equal?
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(a) A = {1, 3}; B = {1, 4}. A and B have different elements,
(b) A = {x: x + 2 = 2} = {0}; B = {0}. A and B have same elements,
(c) A = {1, 3, 4, 4} = {1, 3, 4}; B = {3, 1, 4}. A and B have same elements,
(d) A = { 1,1/2,1/3,... }Correct Option: A
(a) A = {1, 3}; B = {1, 4}. A and B have different elements,
∴ A ≠ B.
(b) A = {x: x + 2 = 2} = {0}; B = {0}. A and B have same elements,
∴ A = B.
(c) A = {1, 3, 4, 4} = {1, 3, 4}; B = {3, 1, 4}. A and B have same elements,
∴ A = B.
(d) A = { 1,1/2,1/3, ................ } ;
B = {1/n : n ε N} = { 1/1,1/2,1/3,...} .
A and B have same elements, ∴ A = B.
- Find the cardinal number of the following set {x: x = 2n, n ∈ N, 4 ≤ x ≤ 11}
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NA
Correct Option: D
NA
- In which of the following cases, A = B?
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NA
Correct Option: B
NA
