Solution: 2013 Fall Midterm - 4

Okay, so let’s write down what we know

• A = blond
  $ |A| = 6 $
• B = green eyes
  $ |B| = 7 $
• It also says "11 are not blonde and do not have green eyes"
  They could be blonde and not have green eyes, green eyes and not blonde, or neither.
  Basically, 11 people are outside the intersection of A and B
  $ |\overline{A \cap B}| = 11 $

We should find the union of A and B

$ | A \cup B | = 20 - 11 = 9 $

Now, let’s use a formula to find the intersection of A and B

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

$ 9 = 6 + 7 - |A \cap B| $

$ |A \cap B| = 4 $