Set Operations and Venn diagrms worksheet - Free Printable

Problem Analysis:

The task involves identifying elements of various sets based on the given Venn diagram. The sets are labeled as follows:
- U: Universal set (all elements in the diagram).
- X: Elements inside the blue circle.
- Y: Elements inside the red circle.
- Intersection (X ∩ Y): Elements in both circles.
- Union (X ∪ Y): Elements in either or both circles.
- Complement (Y' or X'): Elements not in the respective set.

Venn Diagram Breakdown:

- X: Elements inside the blue circle: {2, 5, 7, 9}.
- Y: Elements inside the red circle: {3, 4, 5, 6, 8, 10}.
- Intersection (X ∩ Y): Elements in both circles: {5}.
- Union (X ∪ Y): Elements in either or both circles: {2, 3, 4, 5, 6, 7, 8, 9, 10}.
- Complement of Y (Y'): Elements outside the red circle: {1, 2, 7, 9}.
- Complement of X (X'): Elements outside the blue circle: {3, 4, 6, 8, 10}.

Solution to Each Part:

#### a. \( X \)
Elements in set \( X \):
\[ X = \{2, 5, 7, 9\} \]

#### b. \( Y \)
Elements in set \( Y \):
\[ Y = \{3, 4, 5, 6, 8, 10\} \]

#### c. \( Y' \)
Elements not in set \( Y \) (complement of \( Y \)):
\[ Y' = \{1, 2, 7, 9\} \]

#### d. \( U \)
Elements in the universal set \( U \):
\[ U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \]

#### e. \( X \cup Y \)
Elements in either \( X \) or \( Y \) or both (union of \( X \) and \( Y \)):
\[ X \cup Y = \{2, 3, 4, 5, 6, 7, 8, 9, 10\} \]

#### f. \( X \cap Y \)
Elements in both \( X \) and \( Y \) (intersection of \( X \) and \( Y \)):
\[ X \cap Y = \{5\} \]

#### g. \( X - Y \)
Elements in \( X \) but not in \( Y \):
\[ X - Y = \{2, 7, 9\} \]

#### h. \( Y - X \)
Elements in \( Y \) but not in \( X \):
\[ Y - X = \{3, 4, 6, 8, 10\} \]

#### i. \( (X \cap Y)' \)
Elements not in the intersection of \( X \) and \( Y \) (complement of \( X \cap Y \)):
\[ (X \cap Y)' = \{1, 2, 3, 4, 6, 7, 8, 9, 10\} \]

#### j. \( (X \cup Y)' \)
Elements not in the union of \( X \) and \( Y \) (complement of \( X \cup Y \)):
\[ (X \cup Y)' = \{1\} \]

Final Answers:

\[
\boxed{
\begin{aligned}
a. & \quad X = \{2, 5, 7, 9\} \\
b. & \quad Y = \{3, 4, 5, 6, 8, 10\} \\
c. & \quad Y' = \{1, 2, 7, 9\} \\
d. & \quad U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \\
e. & \quad X \cup Y = \{2, 3, 4, 5, 6, 7, 8, 9, 10\} \\
f. & \quad X \cap Y = \{5\} \\
g. & \quad X - Y = \{2, 7, 9\} \\
h. & \quad Y - X = \{3, 4, 6, 8, 10\} \\
i. & \quad (X \cap Y)' = \{1, 2, 3, 4, 6, 7, 8, 9, 10\} \\
j. & \quad (X \cup Y)' = \{1\}
\end{aligned}
}
\]