Printable worksheet featuring three distinct Venn diagram exercises designed to test understanding of set notation and operations.

Problem: Solve the Problems Using the Venn Diagrams

We will solve each part of the problem step by step using the given Venn diagrams.

---

#### 1) First Venn Diagram (K and L)

The Venn diagram shows two sets, \( K \) and \( L \), with the following regions:
- \( K \cap L \): 4
- \( K - L \): 20 + 16 + 17 = 53
- \( L - K \): 5 + 11 + 1 = 17
- \( K \cap L' \): 20 + 16 + 17 = 53
- \( L \cap K' \): 5 + 11 + 1 = 17

Now, let's solve the questions:

1. \( K \cap L' \):
- This represents the elements in \( K \) but not in \( L \).
- From the diagram: \( K \cap L' = 20 + 16 + 17 = 53 \).

2. \( L - K' \):
- This represents the elements in \( L \) but not in \( K' \), which is the same as \( L \cap K \).
- From the diagram: \( L - K' = 4 \).

3. \( L - K \):
- This represents the elements in \( L \) but not in \( K \).
- From the diagram: \( L - K = 5 + 11 + 1 = 17 \).

4. \( K \):
- This represents all elements in \( K \).
- From the diagram: \( K = 20 + 16 + 17 + 4 = 57 \).

So, the answers are:
\[
\boxed{53, 4, 17, 57}
\]

---

#### 2) Second Venn Diagram (G and H)

The Venn diagram shows two sets, \( G \) and \( H \), with the following regions:
- \( G \cap H \): \( g, h, z \)
- \( G - H \): \( n, x, q \)
- \( H - G \): \( w, r, b \)
- \( G' \cap H' \): \( c, e, a \)

Now, let's solve the questions:

1. \( G \cap H \):
- This represents the elements common to both \( G \) and \( H \).
- From the diagram: \( G \cap H = \{g, h, z\} \).

2. \( G \cap H' \):
- This represents the elements in \( G \) but not in \( H \).
- From the diagram: \( G \cap H' = \{n, x, q\} \).

3. \( H' - G' \):
- This represents the elements not in \( H \) but in \( G \).
- From the diagram: \( H' - G' = \{n, x, q\} \).

4. \( (G - H)' \):
- This represents the complement of the set \( G - H \), which includes all elements not in \( G - H \).
- From the diagram: \( G - H = \{n, x, q\} \).
- The complement \( (G - H)' \) includes all other elements: \( \{c, e, a, g, h, z, w, r, b\} \).

So, the answers are:
\[
\boxed{\{g, h, z\}, \{n, x, q\}, \{n, x, q\}, \{c, e, a, g, h, z, w, r, b\}}
\]

---

#### 3) Third Venn Diagram (A and B)

The Venn diagram shows two sets, \( A \) and \( B \), with the following regions:
- \( A \cap B \): 75
- \( A - B \): 95 + 20 + 55 = 170
- \( B - A \): 65 + 70 + 40 = 175
- \( A' \cap B' \): 25 + 50 + 15 = 90

Now, let's solve the questions:

1. \( A \cup B \):
- This represents all elements in either \( A \) or \( B \) or both.
- From the diagram: \( A \cup B = 95 + 20 + 55 + 75 + 65 + 70 + 40 = 420 \).

2. \( B' \):
- This represents all elements not in \( B \).
- From the diagram: \( B' = 95 + 20 + 55 + 25 + 50 + 15 = 260 \).

3. \( B - A \):
- This represents the elements in \( B \) but not in \( A \).
- From the diagram: \( B - A = 65 + 70 + 40 = 175 \).

4. \( A' \cup B' \):
- This represents all elements not in \( A \) or not in \( B \) (or both).
- From the diagram: \( A' \cup B' = 25 + 50 + 15 + 95 + 20 + 55 + 65 + 70 + 40 = 495 \).

So, the answers are:
\[
\boxed{420, 260, 175, 495}
\]

---

Final Answers:

1. \(\boxed{53, 4, 17, 57}\)
2. \(\boxed{\{g, h, z\}, \{n, x, q\}, \{n, x, q\}, \{c, e, a, g, h, z, w, r, b\}}\)
3. \(\boxed{420, 260, 175, 495}\)