Question

The diagram represents three statements about animals at the zoo: p, q, and r.



For how many animals is (p ∨ q) ∧ r true?

15
17
20
22

Answer 1

I can't see the diagram you mean — could you upload it or give the numbers in each Venn region?

Meanwhile, here is how to get the answer from the diagram:

(p ∨ q) ∧ r = r ∧ (p ∪ q). So count all animals that are in r and also in p or q. Equivalently, add the counts of the three regions inside circle r that overlap p and/or q:
- r ∧ p ∧ ¬q
- r ∧ ¬p ∧ q
- r ∧ p ∧ q

In other words: take the total number in r and subtract the number in the part of r that is neither p nor q (the r-only region).

If you post the diagram or the numbers for those regions I’ll compute which of 15, 17, 20 or 22 is correct.