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 don't see the diagram — could you upload it or tell me the numbers in each region of the Venn diagram?

Meanwhile, here is how to get the answer once you have the region counts:

We want the number of animals for which (p ∨ q) ∧ r is true, i.e. animals that satisfy r and at least one of p or q. In set notation that's (p ∪ q) ∩ r. Two equivalent ways to compute it from the diagram:

1. Add the three regions inside r that also lie in p or q:
- the region r ∩ p only,
- the region r ∩ q only,
- plus the central region r ∩ p ∩ q.
Sum those three numbers.

2. Using intersections:
|(p ∪ q) ∩ r| = |p ∩ r| + |q ∩ r| − |p ∩ q ∩ r|.

If you post the diagram or the counts for the relevant regions, I’ll compute the numeric answer.