Andrew M. answered • 01/20/17

Patient and Insightful Ivy League Math And Science Tutor

Hello again.

(a) You are looking for PT or DH (PT∪DH).

63 like PT, 27 like DH, and 17 like PT and DH.

These numbers include those who like both PT and DH.

If you simply add PT and DH, you end up adding

those who like both twice, so you need to subtract

those who like PT and DH:

PT∪DH = PT + DH - PT∩DH = 63 + 27 - 17 = 73.

(b) Good

(c) It helps if you draw a Venn diagram.

I am new to Wyzant and I don't know how to insert diagrams.

15 like AL only and 25 like AL but not PT,

so, 25 - 15 = 10 like AL and DH but not PT.

17 like PT and DH.

DH = 27 = (AL and DH but not PT) + (DH and PT) + (only DH)

= 10 + 17 + (only DH).

Therefore

**only DH = 0**. That is, no one likes only DH.
Andrew M.

01/20/17