Given that n(m)=50,n(p)=25,and n(mup)=60,calculate n(pnm)
I will assume this deals with sets and you are saying:
n(m)=50,n(p)=25,and n(m ∪ p)=60,calculate n(p ∩ m)
n(p ∩ m) = n(m) + n(p) - n(m ∪ p)
= 50 + 25 - 60 = 15
sketch a Venn diagram to illustrate this result
50+25-60=15
To calculate n(pnm), we need to use the principle of inclusion-exclusion. The formula for the principle of inclusion-exclusion allows us to find the size of the union of multiple sets by considering the sizes of individual sets and their intersections.
The formula is:
n(A U B U C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C)
In this case, the sets we are dealing with are m, p, and mup.
Given:
n(m) = 50
n(p) = 25
n(mup) = 60
Let's substitute these values into the formula:
n(pnm) = n(p) + n(m) + n(mup) - n(p ∩ m) - n(p ∩ mup) - n(m ∩ mup) + n(p ∩ m ∩ mup)
Substituting the given values:
n(pnm) = 25 + 50 + 60 - n(p ∩ m) - n(p ∩ mup) - n(m ∩ mup) + n(p ∩ m ∩ mup)
To further calculate n(pnm), we need information about the intersections between the sets p, m, and mup. Without this information, we cannot determine the exact value of n(pnm).
Please provide the necessary information about the intersections between sets p, m, and mup for a precise calculation.
To calculate n(pnm), we need to understand what the notation represents. The symbol "n" likely represents the number of elements in a set, and the subscripts indicate the sets involved.
Let's break down the given information:
- n(m) = 50: The number of elements in set m is 50.
- n(p) = 25: The number of elements in set p is 25.
- n(m ∪ p) = 60: The number of elements in the union of sets m and p is 60.
From this information, we can infer that the union of sets m and p (m ∪ p) contains both set m and set p, meaning it includes all elements from both sets without any duplicates.
To calculate n(pnm), we need to find the number of elements in the intersection of sets p and m (p ∩ m). However, we don't have this information directly.
To find n(pnm), we can use the principle of inclusion-exclusion:
n(m ∪ p) = n(m) + n(p) - n(m ∩ p)
Since we know n(m ∪ p) = 60, n(m) = 50, and n(p) = 25, we can rearrange the formula to solve for n(m ∩ p):
60 = 50 + 25 - n(m ∩ p)
n(m ∩ p) = 50 + 25 - 60
= 75 - 60
= 15
Now that we know n(m ∩ p) = 15, we can substitute it into the formula for n(pnm):
n(pnm) = n(p ∩ m) = 15
Therefore, n(pnm) is equal to 15.