SOLUTION: Given U = {l, m, n, o, p, q, r, s, t, u, v, w}, A = {l, o, p, q, s, t}, B = {n, o, r, s, v, w}, and C = {l, m, n, q, r, t}, find (A′ U C′) ∩ B ′. I

Algebra ->  sets and operations -> SOLUTION: Given U = {l, m, n, o, p, q, r, s, t, u, v, w}, A = {l, o, p, q, s, t}, B = {n, o, r, s, v, w}, and C = {l, m, n, q, r, t}, find (A′ U C′) ∩ B ′. I      Log On


   

Question 202683: Given U = {l, m, n, o, p, q, r, s, t, u, v, w}, A = {l, o, p, q, s, t}, B = {n, o, r, s, v, w},
and C = {l, m, n, q, r, t},
find (A′ U C′) ∩ B ′.
I really need help on this. I have tried and tried to do this Universal Set U stuff but it is very confusing to me... Please help...
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: to add more to your confusion, the universal set U and the union operator U are actually two different symbols and stand for completely different ideas....


First, let's find A'. So form a set of elements from U but NOT in A:



Now let's find B'. Apply the same technique but form a set of elements from U but NOT from B:




Finally, do the same for C'. Make a set from U but NOT from C:



-----------------


Now let's find :

Combine the sets A' and C' and remove duplicates to get




Now take the common elements from set and B' to get the elements: m, p, and u

Note: these elements are in BOTH sets and B'


So

So the final set we're looking for is