Advertisements
Advertisements
Question
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
(A ∩ B)' = A' ∪ B'
Solution
A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8},
X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
The intersection of A and B includes elements common to both A and B:
A ∩ B = {3, 4}
The complement of A∩B includes all elements in the universal set X that are not in A∩B:
∴ (A ∩ B)' = X − A ∩ B
∴ (A ∩ B)' = {1, 2, 5, 6, 7, 8, 9, 10} ...(i)
The complement of A includes all elements in X that are not in A:
A' = X − A
A' = {5, 6, 7, 8, 9, 10}
The complement of B includes all elements in X that are not in B:
B' = X − B
B' = {1, 2, 7, 8, 9, 10}
The union of A′ and B′ includes all elements that are in either A' or B':
∴ A' ∪ B' = {1, 2, 5, 6, 7, 8, 9, 10} ...(ii)
From (i) and (ii), we get
(A ∩ B)' = A' ∪ B'
APPEARS IN
RELATED QUESTIONS
If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A'∩B') = 5, find: n(A ∩ B)
If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A' ∩ B') = 5, find: n(A' ∩ B)
If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A' ∩ B') = 5, find: n(A ∩ B')
If A, B, C are the sets for the letters in the words 'college', 'marriage' and 'luggage' respective, then verify that [A – (B ∪ C)] = [(A – B) ∩ (A – C)]
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
(A ∪ B) = (A − B) ∪ (A ∩ B) ∪ (B − A)
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
A ∩ (B ∆ C) = (A ∩ B) ∆ (A ∩ C)
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {4, 5, 6, 7, 8} and universal set X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then verify the following:
n(B) = (A' ∩ B) + n(A ∩ B)
Write down the power set of A = {1,2,3}
Solve the following inequality and write the solution set using interval notation
− 9 < 2x + 7 ≤ 19
Solve the following inequality and write the solution set using interval notation
6x2 + 1 ≤ 5x
If A = (–7, 3], B = [2, 6] and C = [4, 9] then find A ∪ B
If A = (–7, 3], B = [2, 6] and C = [4, 9] then find A ∪ C
If A = (–7, 3], B = [2, 6] and C = [4, 9] then find B – C
If A = (–7, 3], B = [2, 6] and C = [4, 9] then find A – B
Select the correct answer from given alternative.
If aN = {ax : x ∈ N}, then set 6N ∩ 8N =
Select the correct answer from given alternative.
If set A is empty set then n[P [P [P (A)]]] is
Select the correct answer from given alternative.
If the two sets A and B are having 43 elements in common, then the number of elements common to each of the sets A × B and B × A is
Answer the following:
If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12} Write down the set A ∪ B
Answer the following:
If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11} C = {3, 5, 8, 9, 12} Write down the set B ∩ C
Answer the following:
If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12} Write down the set A – B
Answer the following:
If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12} Write down the set B ∩ C'
Answer the following:
If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12} Write down the set A ∪ B ∪ C
Answer the following:
If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12} Write down the set A ∩ (B ∪ C)
Answer the following:
If A = {−1, 1} , find A × A × A
