If n(AuBuC)=12 and n(AuB)=8,find n(A'nB'nC). Solution n(A'nB'nC)=12 -8 =4
How did you get the union of the three sets
To find the value of n(A'nB'nC), first, let's understand the notations:
n(AuBuC) represents the total number of elements in the set A, set B, and set C combined.
n(AuB) represents the total number of elements in the set A and set B combined.
n(A'nB'nC) represents the total number of elements that are not in set A, not in set B, and not in set C.
Given that n(AuBuC) is 12 and n(AuB) is 8, we can use these values to find n(A'nB'nC).
n(A'nB'nC) = n(AuBuC) - n(AuB)
= 12 - 8
= 4
Therefore, n(A'nB'nC) is equal to 4.
To find the value of n(A'nB'nC), we need to understand what each term represents.
n(AuBuC) represents the total number of elements in the set A, B, and C combined.
n(AuB) represents the total number of elements in the set A and B combined.
Now, we can use this information to find the value of n(A'nB'nC). Here's how:
Step 1: Find the value of n(A∪B).
Given that n(A∪B) = 8, this means that there are 8 elements in the set A and B combined.
Step 2: Find the value of n(A∪B∪C).
Given that n(A∪B∪C) = 12, this means that there are 12 elements in the set A, B, and C combined.
Step 3: Find the value of n(A'nB'nC).
Since n(A'nB'nC) represents the number of elements that are NOT present in the sets A, B, or C, we can find this value by subtracting the number of elements in the set A∪B from the number of elements in the set A∪B∪C.
Therefore, n(A'nB'nC) = n(A∪B∪C) - n(A∪B).
Substituting the known values, we have:
n(A'nB'nC) = 12 - 8.
Step 4: Calculate the value.
n(A'nB'nC) = 12 - 8 = 4.
Therefore, the value of n(A'nB'nC) is 4.
n(AuBuC)=12
n(AuB)=8, so n(C)=4
n(A'uB'nC)=n((AuB)'nC)
That help?