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Master Set Operation Rules - Beginner Level Problems Set Operation Rules BEGINNER

Excel in competitive exams with this skill builder ⚡ worksheet on Set Operation Rules. Worksheet 3 of 10 contains 20 beginner-level problems. Target your step-by-step problem solving skills while practicing set operation rules practice, set operation rules for competitive exams, and how to solve set operation rules.

📝 Worksheet 3 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner level

What you'll learn in this worksheet:
Your progress through Set Operation Rules
Worksheet 3 of 10 (22% complete)

Question 1

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): − What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: −
- Operation type: Difference (A − B)

RULE HYPOTHESIS:
The rule is a Difference (A − B) operation

SET OPERATION DEFINITION:
Difference (A − B) contains elements in A that are not in B

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Difference (A − B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 2

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): ∪ What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: ∪
- Operation type: Union (A ∪ B)

RULE HYPOTHESIS:
The rule is a Union (A ∪ B) operation

SET OPERATION DEFINITION:
Union (A ∪ B) combines all elements from both sets (no duplicates)

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Union (A ∪ B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 3

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): − What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: −
- Operation type: Difference (A − B)

RULE HYPOTHESIS:
The rule is a Difference (A − B) operation

SET OPERATION DEFINITION:
Difference (A − B) contains elements in A that are not in B

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Difference (A − B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 4

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): ∩ What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: ∩
- Operation type: Intersection (A ∩ B)

RULE HYPOTHESIS:
The rule is a Intersection (A ∩ B) operation

SET OPERATION DEFINITION:
Intersection (A ∩ B) contains only elements common to both sets

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Intersection (A ∩ B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 5

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): ∩ What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: ∩
- Operation type: Intersection (A ∩ B)

RULE HYPOTHESIS:
The rule is a Intersection (A ∩ B) operation

SET OPERATION DEFINITION:
Intersection (A ∩ B) contains only elements common to both sets

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Intersection (A ∩ B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 6

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): ∪ What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: ∪
- Operation type: Union (A ∪ B)

RULE HYPOTHESIS:
The rule is a Union (A ∪ B) operation

SET OPERATION DEFINITION:
Union (A ∪ B) combines all elements from both sets (no duplicates)

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Union (A ∪ B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 7

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): ∩ What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: ∩
- Operation type: Intersection (A ∩ B)

RULE HYPOTHESIS:
The rule is a Intersection (A ∩ B) operation

SET OPERATION DEFINITION:
Intersection (A ∩ B) contains only elements common to both sets

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Intersection (A ∩ B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 8

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): ∪ What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: ∪
- Operation type: Union (A ∪ B)

RULE HYPOTHESIS:
The rule is a Union (A ∪ B) operation

SET OPERATION DEFINITION:
Union (A ∪ B) combines all elements from both sets (no duplicates)

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Union (A ∪ B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 9

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): ∪ What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: ∪
- Operation type: Union (A ∪ B)

RULE HYPOTHESIS:
The rule is a Union (A ∪ B) operation

SET OPERATION DEFINITION:
Union (A ∪ B) combines all elements from both sets (no duplicates)

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Union (A ∪ B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 10

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): − What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: −
- Operation type: Difference (A − B)

RULE HYPOTHESIS:
The rule is a Difference (A − B) operation

SET OPERATION DEFINITION:
Difference (A − B) contains elements in A that are not in B

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Difference (A − B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 11

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): − What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: −
- Operation type: Difference (A − B)

RULE HYPOTHESIS:
The rule is a Difference (A − B) operation

SET OPERATION DEFINITION:
Difference (A − B) contains elements in A that are not in B

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Difference (A − B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 12

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): ∪ What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: ∪
- Operation type: Union (A ∪ B)

RULE HYPOTHESIS:
The rule is a Union (A ∪ B) operation

SET OPERATION DEFINITION:
Union (A ∪ B) combines all elements from both sets (no duplicates)

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Union (A ∪ B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 13

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): − What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: −
- Operation type: Difference (A − B)

RULE HYPOTHESIS:
The rule is a Difference (A − B) operation

SET OPERATION DEFINITION:
Difference (A − B) contains elements in A that are not in B

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Difference (A − B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 14

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): ∩ What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: ∩
- Operation type: Intersection (A ∩ B)

RULE HYPOTHESIS:
The rule is a Intersection (A ∩ B) operation

SET OPERATION DEFINITION:
Intersection (A ∩ B) contains only elements common to both sets

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Intersection (A ∩ B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 15

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): ∪ What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: ∪
- Operation type: Union (A ∪ B)

RULE HYPOTHESIS:
The rule is a Union (A ∪ B) operation

SET OPERATION DEFINITION:
Union (A ∪ B) combines all elements from both sets (no duplicates)

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Union (A ∪ B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 16

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): ∩ What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: ∩
- Operation type: Intersection (A ∩ B)

RULE HYPOTHESIS:
The rule is a Intersection (A ∩ B) operation

SET OPERATION DEFINITION:
Intersection (A ∩ B) contains only elements common to both sets

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Intersection (A ∩ B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 17

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): ∩ What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: ∩
- Operation type: Intersection (A ∩ B)

RULE HYPOTHESIS:
The rule is a Intersection (A ∩ B) operation

SET OPERATION DEFINITION:
Intersection (A ∩ B) contains only elements common to both sets

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Intersection (A ∩ B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 18

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): ∩ What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: ∩
- Operation type: Intersection (A ∩ B)

RULE HYPOTHESIS:
The rule is a Intersection (A ∩ B) operation

SET OPERATION DEFINITION:
Intersection (A ∩ B) contains only elements common to both sets

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Intersection (A ∩ B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 19

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): ∩ What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: ∩
- Operation type: Intersection (A ∩ B)

RULE HYPOTHESIS:
The rule is a Intersection (A ∩ B) operation

SET OPERATION DEFINITION:
Intersection (A ∩ B) contains only elements common to both sets

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Intersection (A ∩ B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements

Question 20

Identify the set operation rule being applied: Figure 1 (Set A): Figure 2 (Set B): Figure 3 (Operation): − What is the result (Figure 4)?
SET THEORY PATTERN ANALYSIS:

Step 1: Identify the sets
- Set A (Figure 1): Elements at specific positions
- Set B (Figure 2): Elements at specific positions

Step 2: Identify overlapping elements
- Compare positions in both sets
- Element at (50, 60) appears in BOTH sets

Step 3: Recognize the operation
- Operation symbol: −
- Operation type: Difference (A − B)

RULE HYPOTHESIS:
The rule is a Difference (A − B) operation

SET OPERATION DEFINITION:
Difference (A − B) contains elements in A that are not in B

APPLICATION:
Set A has elements: {(40, 60), (50, 60)}
Set B has elements: {(50, 60), (70, 60)}

Difference (A − B) result:
- Common elements: {(50, 60)}
- A-only elements: {(40, 60)}
- B-only elements: {(70, 60)}

Result depends on operation:
- Union: All unique = {(40, 60), (50, 60), (70, 60)}
- Intersection: Common only = {(50, 60)}
- Difference: A-only = {(40, 60)}

SET THEORY PRINCIPLES:
- Union: A ∪ B = {x | x ∈ A OR x ∈ B}
- Intersection: A ∩ B = {x | x ∈ A AND x ∈ B}
- Difference: A − B = {x | x ∈ A AND x ∉ B}

COMMON MISTAKES TO AVOID:
- Confusing union with intersection
- Forgetting to remove duplicates in union
- Wrong order in difference operation (A−B ≠ B−A)
- Miscounting common elements
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