For any three sets A, B and C if n(A) = 17 n(B) = 17, n(C) = 17, n (A ∩ B) = 7 n(B ∩ C) = 6, n(A ∩ C) = 5 and n(A ∩ B ∩ C) = 2, find n(A ∪ B ∪ C).

Here we are provided with the cardinality of three set A, B, C along with the cardinality of their intersection and those values are as follows

n(A) = 17

n(B) = 17

n(C) = 17

n(A ∩ B) = 7

n (B ∩ C) = 6

(A ∩ C) = 5

Here we have to find the value of n(A U B U C)

We know that when we have the cardinality of three known sets with the cardinality of their intersections and we have to find the cardinality of A U B U C we can use the formula

n(A U B U C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C)

…… (i)

So using the formula putting the values we will find

n(A U B U C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C)

= 17 + 17 + 17 – 7 – 6 – 5 + 2

= 53 – 18 + 2

= 55 – 20

= 35

So n(A U B U C) = 35