Question

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

Answer 1

For any three sets A, B, C

n(AUBUC)
= n(A) +n(B)+n(C) - n(AUB) - n(BUC) - n(AUC) + n(AnBnC)

n(AUBUC) = 17+17+17 - 7 - 6 - 5 + 2


n(AUBUC) = 51 - 18 +2


n(AUBUC) = 51 - 16


n(AUBUC) = 35




I hope this answer helps you

Answer 2

QUESTION :
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 , (A ∩C)= 5 and n (A ∩ B ∩ C) = 2,find n (A U B U C).

CARDINAL NUMBER OF A FINITE SET :
The Cardinal number of a finite set A is the number of distinct elements in the set A. It is denoted by n(A).
•It is not possible to define the Cardinal number of an infinite set.
•The Cardinal number of the empty set is zero.
•The Cardinal number of a singleton set is 1.

SOLUTION :

GIVEN :
n (A) = 17
n (B) = 17
n (C)=17
n (A ∩ B) = 7
n (B ∩ C) = 6
(A ∩ C)= 5
n (A ∩ B ∩ C) = 2

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)

n (A U B U C) = 17 + 17 + 17 - 7 - 6 - 5 + 2
n (A U B U C) = 53 - 18 + 2
n (A U B U C) = 55 - 20
n (A U B U C) = 35

Hence, n (A U B U C) = 35

HOPE THIS WILL HELP YOU...