Answer :

Here we are given that


A = {4, 5, 6}


B = {5, 6, 7, 8}


C = {6, 7, 8, 9}


Here we have to verify the eqn given below


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)


Here we have to find the cardinality of all the sets and their intersection. So basing on the data given we can find the values for the eqn .


(A Ո B Ո C) will give elements which are common to all the three sets while (A B C) will give combination of all distinct elements


A = {4, 5, 6}


B = {5, 6, 7, 8}


C = {6, 7, 8, 9}


(A Ո B) = {4, 5, 6} Ո {5, 6, 7, 8} = {5, 6}


(B Ո C) = {5, 6, 7, 8} Ո {6, 7, 8, 9} = {6, 7, 8}


(A Ո C) = {4, 5, 6} Ո {6, 7, 8, 9} = {6}


(A Ո B Ո C) = {4, 5, 6} Ո {5, 6, 7, 8} Ո {6, 7, 8, 9} = {6}


(A B C) = {4, 5, 6} {5, 6, 7, 8} {6, 7, 8, 9}


= {4, 5, 6, 7, 8, 9}


So from the above expression we can find the cardinality of all the values,


n(A) = 3


n(B) = 4


n(C) = 4


n(AՈB) = 2


n(BՈC) = 3


n(AՈC) = 1


n(A Ո B Ո C) = 1


n(A B C) = 6


now using 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)


6 = 3 + 4 + 4 – 2 – 3 – 1 + 1


6 = 6 hence verified

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Merchant of Venice (Summary and Important Questions)Merchant of Venice (Summary and Important Questions)Merchant of Venice (Summary and Important Questions)30 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

In a school of 40Tamil Nadu Board - Math

Verify n(A Tamil Nadu Board - Math

In a village of 1Tamil Nadu Board - Math

Verify n(A Tamil Nadu Board - Math

An advertising agTamil Nadu Board - Math

For any three setTamil Nadu Board - Math

In a college, 60 Tamil Nadu Board - Math

In a town 85% of Tamil Nadu Board - Math