# 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) - Mathematics and Statistics

Sum

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)

#### 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}

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)

Concept: Introduction of Set
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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 1 Sets and Relations
Exercise 1.1 | Q 5. (vii) | Page 10