Q. 34.3( 4 Votes )

For any three set

Answer :

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


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