Question

Matilda conducts a survey about what kind of trees people have in their yard.



The Venn diagram describes the results.

Let p: a respondent has oak trees.

Let q: a respondent has pine trees.



The number of respondents for which p ∧ q is true is
.

The number of respondents for which p ∨ q is true is
.

p ˅ q is true in
colored regions.

Answer 1

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

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

- p ∧ q is the number in the overlap (the intersection) of the oak and pine circles (that single region).
- p ∨ q is the number of respondents in the union: sum of the oak-only region, the pine-only region, and the overlap. Equivalently n(p ∨ q) = n(p) + n(q) − n(p ∧ q).
- p ∨ q is true in 3 colored regions (oak-only, pine-only, and the overlap).

If you give the numbers shown in the three regions I’ll fill in the numeric answers.