Question 202683
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:


*[Tex \LARGE A'=\left\{m, n, r, u, v, w\right\}] 


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


*[Tex \LARGE B'=\left\{l, m, p, q, t, u\right\}] 



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


*[Tex \LARGE C'=\left\{o, p, s, u, v, w\right\}] 


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Now let's find *[Tex \LARGE A' \cup C']:


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


*[Tex \LARGE A' \cup C'=\left\{m, n, o, p, r, s, u, v, w\right\}] 



Now take the common elements from set *[Tex \LARGE A' \cup C'] and B' to get the elements: m, p, and u


Note: these elements are in BOTH sets *[Tex \LARGE A' \cup C'] and B'



So *[Tex \LARGE \left(A' \cup C'\right) \cap B' = \left\{m, p, u\right\}]


So the final set we're looking for is 



*[Tex \LARGE \left(A' \cup C'\right) \cap B' = \left\{m, p, u\right\}]