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Question
If U = {x : x ∈ N, x ≤ 10}, A = {2, 3, 4, 8, 10} and B = {1, 2, 5, 8, 10}, then verify that n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
Solution
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {2, 3, 4, 8, 10}, B = {1, 2, 5, 8, 10}
n(U) = 10, n(A) = 5, n(B) = 5
(A ∪ B) = {2, 3, 4, 8, 10} ∪ {1, 2, 5, 8, 10}
= {1, 2, 3, 4, 5, 8, 10}
∴ n(A ∪ B) = 7 ...(1)
(A ∩ B) = {2, 3, 4, 8, 10} ∩ {1, 2, 5, 8, 10}
= {2, 8, 10}
n(A ∩ B) = 3
n(A) + n(B) – n(A∩B) = 5 + 5 – 3
= 10 – 3
= 7 ...(2)
From (1) and (2) we get,
n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
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