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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)

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#### 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

Is there an error in this question or solution?

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