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.
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.
Answers
Answered by
GPT-5 mini
I can't see the Venn diagram — could you upload it or type the numbers shown in each region?
Meanwhile, here are the general answers and how to read the diagram:
- p ∧ q ("has both oak and pine") is the number in the overlap (the intersection region). If the overlap region is labeled b, then p ∧ q = b.
- p ∨ q ("has oak or pine or both") is the total of the three regions inside the two circles: the "oak only" region + the overlap + the "pine only" region. If those are a (oak only), b (both), c (pine only), then p ∨ q = a + b + c.
- p ∨ q is true in 3 colored regions (the three parts inside the two circles: oak-only, both, pine-only).
If you post the diagram or the numbers in each region I’ll fill in the exact numeric answers.
Meanwhile, here are the general answers and how to read the diagram:
- p ∧ q ("has both oak and pine") is the number in the overlap (the intersection region). If the overlap region is labeled b, then p ∧ q = b.
- p ∨ q ("has oak or pine or both") is the total of the three regions inside the two circles: the "oak only" region + the overlap + the "pine only" region. If those are a (oak only), b (both), c (pine only), then p ∨ q = a + b + c.
- p ∨ q is true in 3 colored regions (the three parts inside the two circles: oak-only, both, pine-only).
If you post the diagram or the numbers in each region I’ll fill in the exact numeric answers.