Solution: 2017 Fall Final - 6

• Let D be the set of students that like Donald Trump
  $ |D| = 13 $
• Let B be the set of students that like Justin Bieber
  $ |B| = 25 $
• Let $ D \cap B $ be the set of students that like both Donald Trump and Justin Bieber
  $ |D \cap B| = 8 $

Let’s find $ |D \cup B| $

$ |D \cup B| = |D| + |B| - |D \cap B| $

$ |D \cup B| = 13 + 25 - 8 $

$ |D \cup B| = 30 $

We’re looking for $ | \overline{D} \cap \overline{B} | = 100 - |D \cup B| $

$ | \overline{D} \cap \overline{B} | = 100 - 30 $

$ | \overline{D} \cap \overline{B} | = 70 $