If A,B and C are three sets,each having a finite number of element,find the value of N(AuB)n (AuC) from the following information,N(AuBuC)=100,N(AnBnC)=10,N(AuBuC)=25,N(AnB)=N(BnC)=15,N(A)=N(C)=2(n(B)
well, you know that
n(AUB) = n(A) + n(B) - n(A∩B)
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Answer
30
To find the value of N(A∪B)∩(A∪C), we will use the principle of inclusion-exclusion and the given information.
Let's break down the problem step by step:
1. Start with the principle of inclusion-exclusion:
N(A∪B∪C) = N(A) + N(B) + N(C) - N(A∩B) - N(A∩C) - N(B∩C) + N(A∩B∩C)
2. Substitute the given values:
N(A∪B∪C) = 100 (given)
N(A∩B∩C) = 10 (given)
N(A∩B) = N(B∩C) = 15 (given)
N(A) = N(C) = 2 * N(B) (given)
Note: Since we don't have the exact values of N(A), N(B), and N(C), we can express them in terms of a variable, let's say n.
N(A) = 2n
N(C) = 2n
N(B) = n
3. Substitute the values into the principle of inclusion-exclusion:
100 = 2n + n + 2n - 15 - 15 + 10
Simplifying the equation:
100 = 5n - 20
Add 20 to both sides:
120 = 5n
Divide both sides by 5:
n = 24
Now we can find the value of N(A∪B)∩(A∪C):
N(A∪B)∩(A∪C) = N(A∪B∪C) - N(A∩B∩C)
N(A∪B)∩(A∪C) = 100 - 10
N(A∪B)∩(A∪C) = 90
Therefore, the value of N(A∪B)∩(A∪C) is 90.