Question

Verify n (A $\cup$ B $\cup$ C) = n (A) + n(B) + n (C) – n(A $\cap$ B) – (B $\cap$ C) – n(A $\cap$ C) + (A $\cap$ B $\cup$ C) for the following sets A = {1, 3, 5, 6, 8}, B = {3, 4, 5, 6} and C = {1, 2, 3, 6}

Answer 1

(A $\cup$ B $\cup$ C) = {1,2, 3, 4, 5, 6, 8}

n (A $\cup$ B $\cup$ C) = 7

Also, n (A) = 5, n (B) = 4, n (C) = 4,

Further, A $\cap$ B = {3, 5, 6} $\Rightarrow$ n(A $\cap$ B) = 3

B $\cap$ C = {3, 6} $\Rightarrow$ n(B $\cap$ C) = 2

A $\cap$ C = {3, 5, 6} $\Rightarrow$ n(A $\cap$ C) = 3

Also, A $\cap$ B $\cap$ C = {3, 6} $\Rightarrow$ n(A $\cap$ B $\cap$ C) = 2

Now n (A $\cup$ B $\cup$ C) = n (A) + n (B) + n (C) – n(A $\cap$ B) – n( B $\cap$ C) – n (A $\cap$ C) + n(A $\cap$ B $\cap$ C)

7 = 5 + 4 + 4 – 3 – 2 – 3 + 2

7 = 13 – 8 + 2

7 = 5 + 2

7 = 7


Thus verified