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Let A  and W  be sets. Suppose n(A′)=17, n(W)=12  , n(A′∪W′)=25 and n(A∩W)=3. What is n(U)

 Dec 6, 2018
 #1
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\(U=(A\cap W) \cup (A \cap W)^\prime\\ (A \cap W) \cap (A \cap W)^\prime = \emptyset \Rightarrow \\ |U| = |(A\cap W)|+|(A \cap W)^\prime|\\ |A\cap W| =3\\ |(A\cap W)^\prime| = |(A^\prime \cup W^\prime)| = 25\\ |U| = 3 + 25 = 28 \)

 

as far as I can see the other details aren't needed.

 Dec 6, 2018

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