Question 945966: Let U = {a, b, c, d, e, f} be the universal set and let A and B be subsets of U. Suppose further that
A ∩ B' = {b}, A ∪ B = {a, b, c, d, f}, and A' = {a, e, f}.
Find B.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! A' = {a, e, f} is given
A = {b, c, d} start with set U and erase everything in A'
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We have A ∩ B' = {b}
So that means that the element 'b' is in both set A and in set B'
Since 'b' is in set B', this means set B itself does not have 'b' inside it.
What else could be in set B? Well look at A ∪ B = {a, b, c, d, f}
We know A = {b, c, d} from above.
Since A ∪ B = {a, b, c, d, f}, we need an 'a' and an 'f' to fill out A ∪ B completely.
So set B must have {a,f} at the very least. Could set B have c or d in it? It's possible since a set union can combine two sets with duplicate elements. The duplicates are tossed out.
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So here are all the possibilities for set B
B = {a, f}
B = {a, c, f}
B = {a, d, f}
B = {a, c, d, f}
Each possible set B has 'a' and 'f' in it.
It's great that we have all the possible sets for B, but unfortunately we don't have enough information to narrow down the answer to just one set.
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