Venn Diagram - Two Circles worksheet for practicing set operations.

To solve the problems in the Venn diagram worksheet, we need to carefully analyze each diagram and use the information provided in the overlapping regions to determine the values for the sets. Let's go through each problem step by step.

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Problem 1:

The first Venn diagram has two circles labeled \( A \) and \( B \). The regions are filled as follows:
- Region outside both circles: 3
- Region inside \( A \) only: 2
- Region inside \( B \) only: 4
- Region inside both \( A \) and \( B \): 1

#### Fill in the blanks:
1. \( A \cup B \): This represents the union of sets \( A \) and \( B \), which includes all elements in either \( A \) or \( B \) or both.
\[
A \cup B = 2 + 1 + 4 = 7
\]

2. \( A \cap B \): This represents the intersection of sets \( A \) and \( B \), which includes elements common to both \( A \) and \( B \).
\[
A \cap B = 1
\]

3. \( A - B \): This represents the elements in \( A \) but not in \( B \).
\[
A - B = 2
\]

4. \( B - A \): This represents the elements in \( B \) but not in \( A \).
\[
B - A = 4
\]

#### Final answers for Problem 1:
\[
\boxed{A \cup B = 7, A \cap B = 1, A - B = 2, B - A = 4}
\]

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Problem 2:

The second Venn diagram has two circles labeled \( C \) and \( D \). The regions are filled as follows:
- Region outside both circles: 6
- Region inside \( C \) only: 8
- Region inside \( D \) only: 5
- Region inside both \( C \) and \( D \): 4

#### Fill in the blanks:
1. \( C \cup D \): This represents the union of sets \( C \) and \( D \), which includes all elements in either \( C \) or \( D \) or both.
\[
C \cup D = 8 + 4 + 5 = 17
\]

2. \( C \cap D \): This represents the intersection of sets \( C \) and \( D \), which includes elements common to both \( C \) and \( D \).
\[
C \cap D = 4
\]

3. \( C - D \): This represents the elements in \( C \) but not in \( D \).
\[
C - D = 8
\]

4. \( D - C \): This represents the elements in \( D \) but not in \( C \).
\[
D - C = 5
\]

#### Final answers for Problem 2:
\[
\boxed{C \cup D = 17, C \cap D = 4, C - D = 8, D - C = 5}
\]

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Problem 3:

The third Venn diagram has two circles labeled \( E \) and \( F \). The regions are filled as follows:
- Region outside both circles: 21
- Region inside \( E \) only: 14
- Region inside \( F \) only: 12
- Region inside both \( E \) and \( F \): 10

#### Fill in the blanks:
1. \( E \cup F \): This represents the union of sets \( E \) and \( F \), which includes all elements in either \( E \) or \( F \) or both.
\[
E \cup F = 14 + 10 + 12 = 36
\]

2. \( E \cap F \): This represents the intersection of sets \( E \) and \( F \), which includes elements common to both \( E \) and \( F \).
\[
E \cap F = 10
\]

3. \( E - F \): This represents the elements in \( E \) but not in \( F \).
\[
E - F = 14
\]

4. \( F - E \): This represents the elements in \( F \) but not in \( E \).
\[
F - E = 12
\]

#### Final answers for Problem 3:
\[
\boxed{E \cup F = 36, E \cap F = 10, E - F = 14, F - E = 12}
\]

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Final Answer Summary:

\[
\boxed{
\begin{aligned}
&\text{Problem 1: } A \cup B = 7, A \cap B = 1, A - B = 2, B - A = 4 \\
&\text{Problem 2: } C \cup D = 17, C \cap D = 4, C - D = 8, D - C = 5 \\
&\text{Problem 3: } E \cup F = 36, E \cap F = 10, E - F = 14, F - E = 12
\end{aligned}
}
\]