Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Sure, let's go through the steps to solve the given set operations problem.
### 1. Draw a Venn Diagram
To draw a Venn diagram representing the universal set [tex]\( U \)[/tex] and the sets [tex]\( D \)[/tex], [tex]\( E \)[/tex], and [tex]\( F \)[/tex], we need to place each element in the appropriate region where these sets intersect or do not intersect.
- Universal Set [tex]\( U \)[/tex]: \{2, 4, 6, 8, 10, 12, 14, 16, 18\}
- Set [tex]\( D \)[/tex]: \{2, 4, 6, 8, 10\}
- Set [tex]\( E \)[/tex]: \{2, 4, 14, 16, 18\}
- Set [tex]\( F \)[/tex]: \{4, 10, 12, 16\}
When drawing the Venn diagram:
- Place 4 in the intersection of all three sets [tex]\(D\)[/tex], [tex]\(E\)[/tex], and [tex]\(F\)[/tex].
- Place other elements considering their presence in the combinations of sets (D, E, F).
Given that creating a visual Venn diagram is outside the scope of text format, you can visualize three overlapping circles, one each for [tex]\(D\)[/tex], [tex]\(E\)[/tex], and [tex]\(F\)[/tex], with their elements appropriately placed in the intersections.
### 2. Find [tex]\( D - (E \cup F) \)[/tex] and [tex]\( (E \cup F) - D \)[/tex]
#### Step-by-Step Solution:
Step 1: Calculate [tex]\( E \cup F \)[/tex]
The union of sets [tex]\( E \)[/tex] and [tex]\( F \)[/tex] is a set containing all unique elements that are in either [tex]\( E \)[/tex] or [tex]\( F \)[/tex] or in both.
[tex]\[ E \cup F = \{2, 4, 14, 16, 18\} \cup \{4, 10, 12, 16\} = \{2, 4, 10, 12, 14, 16, 18\} \][/tex]
Step 2: Calculate [tex]\( D - (E \cup F) \)[/tex]
This is the set of elements that are in [tex]\( D \)[/tex] but not in [tex]\( (E \cup F) \)[/tex].
Given:
[tex]\[ D = \{2, 4, 6, 8, 10\} \][/tex]
[tex]\[ E \cup F = \{2, 4, 10, 12, 14, 16, 18\} \][/tex]
Now, find the difference:
[tex]\[ D - (E \cup F) = \{6, 8\} \][/tex]
Step 3: Calculate [tex]\( (E \cup F) - D \)[/tex]
This is the set of elements that are in [tex]\( (E \cup F) \)[/tex] but not in [tex]\( D \)[/tex].
[tex]\[ E \cup F = \{2, 4, 10, 12, 14, 16, 18\} \][/tex]
[tex]\[ D = \{2, 4, 6, 8, 10\} \][/tex]
Now, find the difference:
[tex]\[ (E \cup F) - D = \{12, 14, 16, 18\} \][/tex]
### Final Results:
[tex]\[ D - (E \cup F) = \{6, 8\} \][/tex]
[tex]\[ (E \cup F) - D = \{12, 14, 16, 18\} \][/tex]
Thus, the detailed step-by-step solution demonstrates that:
[tex]\[ D - (E \cup F) = \{6, 8\} \][/tex]
[tex]\[ (E \cup F) - D = \{12, 14, 16, 18\} \][/tex]
### 1. Draw a Venn Diagram
To draw a Venn diagram representing the universal set [tex]\( U \)[/tex] and the sets [tex]\( D \)[/tex], [tex]\( E \)[/tex], and [tex]\( F \)[/tex], we need to place each element in the appropriate region where these sets intersect or do not intersect.
- Universal Set [tex]\( U \)[/tex]: \{2, 4, 6, 8, 10, 12, 14, 16, 18\}
- Set [tex]\( D \)[/tex]: \{2, 4, 6, 8, 10\}
- Set [tex]\( E \)[/tex]: \{2, 4, 14, 16, 18\}
- Set [tex]\( F \)[/tex]: \{4, 10, 12, 16\}
When drawing the Venn diagram:
- Place 4 in the intersection of all three sets [tex]\(D\)[/tex], [tex]\(E\)[/tex], and [tex]\(F\)[/tex].
- Place other elements considering their presence in the combinations of sets (D, E, F).
Given that creating a visual Venn diagram is outside the scope of text format, you can visualize three overlapping circles, one each for [tex]\(D\)[/tex], [tex]\(E\)[/tex], and [tex]\(F\)[/tex], with their elements appropriately placed in the intersections.
### 2. Find [tex]\( D - (E \cup F) \)[/tex] and [tex]\( (E \cup F) - D \)[/tex]
#### Step-by-Step Solution:
Step 1: Calculate [tex]\( E \cup F \)[/tex]
The union of sets [tex]\( E \)[/tex] and [tex]\( F \)[/tex] is a set containing all unique elements that are in either [tex]\( E \)[/tex] or [tex]\( F \)[/tex] or in both.
[tex]\[ E \cup F = \{2, 4, 14, 16, 18\} \cup \{4, 10, 12, 16\} = \{2, 4, 10, 12, 14, 16, 18\} \][/tex]
Step 2: Calculate [tex]\( D - (E \cup F) \)[/tex]
This is the set of elements that are in [tex]\( D \)[/tex] but not in [tex]\( (E \cup F) \)[/tex].
Given:
[tex]\[ D = \{2, 4, 6, 8, 10\} \][/tex]
[tex]\[ E \cup F = \{2, 4, 10, 12, 14, 16, 18\} \][/tex]
Now, find the difference:
[tex]\[ D - (E \cup F) = \{6, 8\} \][/tex]
Step 3: Calculate [tex]\( (E \cup F) - D \)[/tex]
This is the set of elements that are in [tex]\( (E \cup F) \)[/tex] but not in [tex]\( D \)[/tex].
[tex]\[ E \cup F = \{2, 4, 10, 12, 14, 16, 18\} \][/tex]
[tex]\[ D = \{2, 4, 6, 8, 10\} \][/tex]
Now, find the difference:
[tex]\[ (E \cup F) - D = \{12, 14, 16, 18\} \][/tex]
### Final Results:
[tex]\[ D - (E \cup F) = \{6, 8\} \][/tex]
[tex]\[ (E \cup F) - D = \{12, 14, 16, 18\} \][/tex]
Thus, the detailed step-by-step solution demonstrates that:
[tex]\[ D - (E \cup F) = \{6, 8\} \][/tex]
[tex]\[ (E \cup F) - D = \{12, 14, 16, 18\} \][/tex]
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.
