If n(A)=12 and n(B)=10 and n(AuB)=17. Find n(AnB)
Answers
17=12+10-n(AnB)
n(AnB)=5
Answer:
Step-by-step explanation:
Given values are
n(A) = 12, n(B) = 10 and n(AUB) = 17
- Let us suppose
A be the set of students who only like Chocolates.
B be the set of students who only like Biscuits.
- According to given condition
The no. of students who only like Chocolates = n(A) = 12
The no. of students who only like Biscuits = n(B) = 10
The no. of students who likes either chocolates or Biscuits = n(AUB) = 17
now we need to find the value of n(A∩B)
The no. of students who like both Chocolates and Biscuits = n(A∩B)
We have a formula from the Set Operations.
n(AUB) = n(A) + n(B) - n(A∩B)
So, we can write it as
n(A∩B) = n(A) + n(B) - n(AUB)
now substitute the values n(A) = 12, n(B) = 10 and n(AUB) = 17 in the above equation
n(A∩B) = 12 + 10 - 17
= 22-17
= 5
Hence, n(A∩B) = 5.
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