Thank you for visiting The table shows some trees that are in two city parks Let tex U tex be the smallest possible set that includes all the trees. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To solve the problem of finding [tex]\( R \cap S \)[/tex], which represents the set of trees that are present in both Riverside Park and Sleepy Hollow Park, we need to list the trees from both parks and identify which ones appear in both lists.
Let's break it down step by step:
1. Identify the trees in each park:
- Riverside Park trees are: Aspen (a), Oak (o), Cherry (c), Dogwood (d), Maple (m).
- Sleepy Hollow Park trees are: Dogwood (d), Sycamore (s), Aspen (a), Pine (p), Oak (o).
2. Look for common trees:
We need to find which trees are present in both Riverside Park and Sleepy Hollow Park. This means we are looking for the intersection of the sets of trees from each park.
3. List the common trees:
- Aspen (a) is present in both Riverside Park and Sleepy Hollow Park.
- Dogwood (d) is present in both Riverside Park and Sleepy Hollow Park.
- Oak (o) is present in both Riverside Park and Sleepy Hollow Park.
4. Write the intersection of the two sets:
Therefore, the set [tex]\( R \cap S \)[/tex] contains the trees that are common to both parks. The elements in this set are:
[tex]\[
R \cap S = \{ a, d, o \}
\][/tex]
This set, [tex]\(\{ a, d, o \}\)[/tex], represents the trees found in both Riverside Park and Sleepy Hollow Park: Aspen, Dogwood, and Oak.
Let's break it down step by step:
1. Identify the trees in each park:
- Riverside Park trees are: Aspen (a), Oak (o), Cherry (c), Dogwood (d), Maple (m).
- Sleepy Hollow Park trees are: Dogwood (d), Sycamore (s), Aspen (a), Pine (p), Oak (o).
2. Look for common trees:
We need to find which trees are present in both Riverside Park and Sleepy Hollow Park. This means we are looking for the intersection of the sets of trees from each park.
3. List the common trees:
- Aspen (a) is present in both Riverside Park and Sleepy Hollow Park.
- Dogwood (d) is present in both Riverside Park and Sleepy Hollow Park.
- Oak (o) is present in both Riverside Park and Sleepy Hollow Park.
4. Write the intersection of the two sets:
Therefore, the set [tex]\( R \cap S \)[/tex] contains the trees that are common to both parks. The elements in this set are:
[tex]\[
R \cap S = \{ a, d, o \}
\][/tex]
This set, [tex]\(\{ a, d, o \}\)[/tex], represents the trees found in both Riverside Park and Sleepy Hollow Park: Aspen, Dogwood, and Oak.
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