In a pet shelter for cats only, there were 45 black cats, 30 long-haired cats, and 30 cats who were old (> 10 years old). For this study, cats in the shelter were classified as black/not-black, young/old, and long-haired/short-haired. 12 cats were black, young and long-haired, 10 were black, short-haired and old, 5 were black, long-haired and old, and none of the cats were long-haired, non-black and old.

a. How many total cats were in this shelter (i. e., how many cats were black or long-haired or old)?

b. How many cats were black, short-haired, and young?

c. How many cats were long-haired, not-black, and young?

d. How many cats were short-haired, not-black, and old?

Note: Define your events first (cat is black, cat is long-haired, and cat is old), and show your work using equations or Venn diagrams.