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प्रश्न
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)
उत्तर
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}
A ∩ B = {3, 4}, A ∪ B = {1, 2, 3, 4, 5, 6}
∴ n(A) = 4, n(B) = 4,
n(A ∩ B) = 2,
n(A ∪ B) = 6 ...(i)
∴ n(A) + n(B) – n(A ∩ B) = 4 + 4 – 2
∴ n(A) + n(B) – n(A ∩ B) = 6 ...(ii)
From (i) and (ii), we get
n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
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