For this exercise, let A and B be subsets of a universal set U and suppose n(U)= 200, n(A)= 100, n(B)= 80, and n (A∩B)=40. Compute:
n (A U B)
For this exercise would I compute it by using the addition rule?
n(A U B) = n(A) +n(B) - n (A ∩ B)
n(A U B) = 100 + 80 - 40
=180-40=140
n(AUB) =140
Well, if n(A) is 100, n(B) is 80, and n(A∩B) is 40, then the way to calculate n(A U B) is indeed to use the addition rule. So, you're correct!
n(A U B) = n(A) + n(B) - n(A ∩ B)
= 100 + 80 - 40
= 180 - 40
= 140
So, n(A U B) is 140. Great job! You nailed it! *clownishly applauds*
Yes, you are correct! To compute the number of elements in the union of sets A and B, you can use the addition rule.
The addition rule states that the number of elements in the union of two sets is equal to the sum of the number of elements in each set, minus the number of elements in their intersection.
Using the given information:
n(A U B) = n(A) + n(B) - n(A ∩ B)
n(A U B) = 100 + 80 - 40
n(A U B) = 180 - 40
n(A U B) = 140
Therefore, the number of elements in the union of sets A and B is 140.
Yes, you can use the addition rule to compute n(A U B). The addition rule states that the size of the union of two sets is equal to the sum of the sizes of the individual sets minus the size of their intersection.
To calculate n(A U B), you start by taking the sum of the sizes of A and B: n(A) + n(B). In this case, n(A) is 100 and n(B) is 80, so the sum is 100 + 80 = 180.
However, we have double-counted the elements that are in both A and B because they are included in both n(A) and n(B). To correct this, we subtract the size of their intersection, n(A ∩ B), which is given as 40.
So, the final calculation for n(A U B) is: 180 - 40 = 140.
Therefore, n(A U B) is equal to 140.