Given the following , determine the set ( A' U B) n ( A U B)'

Question

U={1,2,3,4,5,6,7,8}

A={1,3,4,7,8}

B={1,2,4,5}

 

(A'∪ B') ∩ ( A ∪ B)' =

Answer 1

OK. (A' ∪ B') means all not in A but in U, AND all not in B but in U. That's {2, 5, 6} ∪ {3, 6, 7, 8} or {2, 5, 6, 7, 8}.

 

Now, (A ∪ B)' means whatever is NOT in both A and B (but is still in U. That's {3, 5, 6, 7, 8}.

 

The intersection of the two sets found above is next. What is in both? {5, 6, 7, 8}. Cheers!