n[(A intersection Bc) U (Ac intersection B)]

Separate problems unrelated to the image:

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 intersection B) = 40. Compute:

1. n(A U B)
2. n(A intersection Bc)

[the tiny c's are supposed to be superscript]

Help!

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CrackWaffles

n(A intersection Bc) = n(A) -  n(A intersection B) = 100 - 40 = 60
n(B intersection Ac) = n(B) -  n(A intersection B) = 80 - 40 = 40
n(A U B) = n(A intersection Bc) + n(B intersection Ac) + n(A intersection B) = 60 + 40 + 40 = 140
Or, another formula:
n(A U B) = n(A) + n(B) - n(A intersection B) = 100 + 80 - 40 = 140 (same answer).

For the other problem,

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From the picture shown, I gather that 12 is the number of A not in B, i.e.
n(A intersection Bc) = 12
and similarly,
n(Ac intersection B) = 15
Since these two don't intersect,
n[(A intersection Bc) U (Ac intersection B)] = 12 + 15 = 17

n(A intersection Bc) = n(A) - n(A intersection B) = 100 - 40 = 60
n(B intersection Ac) = n(B) - n(A intersection B) = 80 - 40 = 40
n(A U B) = n(A intersection Bc) + n(B intersection Ac) + n(A intersection B) = 60 + 40 + 40 = 140
Or, another formula:
n(A U B) = n(A) + n(B) - n(A intersection B) = 100 + 80 - 40 = 140 (same answer).

For the other problem,

 

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140 is correct for n(A U B), thank you. The other two aren't right though, I tried inputting those answers and it still shows as wrong.

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CrackWaffles

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From the picture shown, I gather that 12 is the number of A not in B, i.e.
n(A intersection Bc) = 12
and similarly,
n(Ac intersection B) = 15
Since these two don't intersect,
n[(A intersection Bc) U (Ac intersection B)] = 12 + 15 = 17

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Herman, 12 + 15 = 27, not 17 (duh!).

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