Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

SET OPERATIONS

- Two or More Set Operations

Given:
[tex]\[
\begin{array}{l}
U = \{2, 4, 6, 8, 10, 12, 14, 16, 18\} \\
D = \{2, 4, 6, 8, 10\} \\
E = \{2, 4, 14, 16, 18\} \\
F = \{4, 10, 12, 16\}
\end{array}
\][/tex]

1. Draw a Venn diagram to represent [tex]\( U \)[/tex], set [tex]\( D \)[/tex], set [tex]\( E \)[/tex], and set [tex]\( F \)[/tex].
2. Find [tex]\( D - (E \cup F) \)[/tex] and [tex]\( (E \cup F) - D \)[/tex]

Sagot :

GinnyAnswer
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]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.