Rule Detection - Beginner-Intermediate Level: visual logic BEGINNER-INTERMEDIATE

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

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

ABSTRACT RELATIONSHIP ANALYSIS:

Step 1: Analyze the relationship between Figure 1 and Figure 2
- Figure 1: Triangle
- Figure 2: 3 circles

Step 2: Identify properties of Figure 1
- Shape: Triangle
- Number of corners/vertices: 3
- Number of sides: 3

Step 3: Identify properties of Figure 2
- Shape: Circles
- Count: 3

RELATIONSHIP HYPOTHESIS:
The count of shapes in Figure 2 equals the number of corners in Figure 1

Step 4: Formulate the rule
Rule: "The second figure in each pair contains as many shapes as the first figure has corners"

VERIFICATION:
- Figure 1: Triangle has 3 corners
- Figure 2: Shows 3 circles ✓
- Relationship confirmed!

APPLICATION TO NEW PAIR:
- Figure 3: Square has 4 corners
- Figure 4 should: Show 4 shapes (circles)

ABSTRACT REASONING PRINCIPLES:
- Look beyond geometric transformations
- Consider numerical relationships
- Examine property mappings (corners → count)
- Test hypothesis on known pairs
- Apply verified rule to new cases

RELATIONSHIP DETECTION STRATEGIES:
1. Identify all properties of source figure
2. Identify all properties of target figure
3. Look for numerical correspondences
4. Check property-to-property mappings
5. Formulate relationship rule
6. Verify on all given pairs
7. Apply to predict unknown

COMMON MISTAKES TO AVOID:
- Looking only for visual transformations
- Missing abstract numerical relationships
- Not considering shape properties (corners, sides, etc.)
- Assuming relationship must be geometric
- Not verifying hypothesis on all pairs

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

PATTERN ANALYSIS:
Step 1: Compare consecutive figures - observe the orientation changes
Step 2: Measure rotation angle between Figure 1 and Figure 2 = 45°
Step 3: Verify this pattern: Figure 2→3 also shows 45° rotation
Step 4: Verify Figure 3→4 also follows the same 45° rotation

RULE HYPOTHESIS:
The figure rotates clockwise by 45° in each step

VERIFICATION:
- Figure 1 to 2: 45° clockwise ✓
- Figure 2 to 3: 45° clockwise ✓
- Figure 3 to 4: 45° clockwise ✓

APPLICATION:
Figure 5 should be Figure 4 rotated clockwise by 45°
Total rotation from start = 180°

COMMON MISTAKES TO AVOID:
- Confusing clockwise with counterclockwise rotation
- Measuring rotation incorrectly
- Assuming different rotation angles

PATTERN ANALYSIS:
Step 1: Examine the fill/shading in each figure
Step 2: Look for systematic changes in shading

RULE HYPOTHESIS:
The shading pattern adds one more filled segment each time

VERIFICATION:
Check pattern consistency across all four figures ✓

APPLICATION:
Based on the identified rule, the next figure should continue the pattern

SHADING ANALYSIS TECHNIQUES:
- Check for binary patterns (filled/unfilled)
- Look for cyclic color patterns
- Count filled vs unfilled elements
- Observe progressive filling patterns
- Check for symmetry in shading

COMMON MISTAKES TO AVOID:
- Missing subtle shading differences
- Not recognizing cyclic patterns
- Assuming random shading changes
- Overlooking progressive patterns

ABSTRACT RELATIONSHIP ANALYSIS:

Step 1: Analyze the relationship between Figure 1 and Figure 2
- Figure 1: Triangle
- Figure 2: 3 circles

Step 2: Identify properties of Figure 1
- Shape: Triangle
- Number of corners/vertices: 3
- Number of sides: 3

Step 3: Identify properties of Figure 2
- Shape: Circles
- Count: 3

RELATIONSHIP HYPOTHESIS:
The count of shapes in Figure 2 equals the number of corners in Figure 1

Step 4: Formulate the rule
Rule: "The second figure in each pair contains as many shapes as the first figure has corners"

VERIFICATION:
- Figure 1: Triangle has 3 corners
- Figure 2: Shows 3 circles ✓
- Relationship confirmed!

APPLICATION TO NEW PAIR:
- Figure 3: Square has 4 corners
- Figure 4 should: Show 4 shapes (circles)

ABSTRACT REASONING PRINCIPLES:
- Look beyond geometric transformations
- Consider numerical relationships
- Examine property mappings (corners → count)
- Test hypothesis on known pairs
- Apply verified rule to new cases

RELATIONSHIP DETECTION STRATEGIES:
1. Identify all properties of source figure
2. Identify all properties of target figure
3. Look for numerical correspondences
4. Check property-to-property mappings
5. Formulate relationship rule
6. Verify on all given pairs
7. Apply to predict unknown

COMMON MISTAKES TO AVOID:
- Looking only for visual transformations
- Missing abstract numerical relationships
- Not considering shape properties (corners, sides, etc.)
- Assuming relationship must be geometric
- Not verifying hypothesis on all pairs

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

PATTERN ANALYSIS:
Step 1: Track the position of the dot in each figure
- Figure 1: Position at (40, 60)
- Figure 2: Position at (60, 40)
- Figure 3: Position at (80, 60)
- Figure 4: Position at (60, 80)

Step 2: Analyze movement vectors
- Fig 1→2: Δx = 20, Δy = -20
- Fig 2→3: Δx = 20, Δy = 20
- Fig 3→4: Δx = -20, Δy = 20

Step 3: Detect movement pattern
The dot follows a spiral inward pattern

RULE HYPOTHESIS:
Systematic positional movement following spiral inward pattern

VERIFICATION:
All movements conform to the identified pattern ✓

APPLICATION:
Next position: (50, 60)
Following the established spiral inward pattern

ADVANCED TECHNIQUES:
- Plot positions on coordinate system
- Check for symmetry and periodicity
- Analyze velocity and acceleration vectors
- Consider boundary conditions

COMMON MISTAKES TO AVOID:
- Assuming simple linear movement
- Not considering boundary reflections
- Missing rotational or circular patterns
- Ignoring spatial constraints

HIERARCHICAL RULE DETECTION:

LEVEL 1 ANALYSIS - Outer Shape Pattern:
Step 1: Identify shapes by counting sides
- Figure 1: Triangle (3 sides)
- Figure 2: Square (4 sides)
- Figure 3: Pentagon (5 sides)
- Figure 4: Hexagon (6 sides)

Rule 1 (Outer): Shape gains +1 side per step

LEVEL 2 ANALYSIS - Inner Element Pattern:
Step 2: Count dots inside each shape
- Figure 1: 1 dot
- Figure 2: 2 dots
- Figure 3: 3 dots
- Figure 4: 4 dots

Rule 2 (Inner): Number of dots increases by +1 per step

NESTED RULE HYPOTHESIS:
TWO independent hierarchical rules:
1. Outer rule: Polygon sides = 3, 4, 5, 6, ...
2. Inner rule: Dot count = 1, 2, 3, 4, ...

CORRELATION CHECK:
Both patterns follow same arithmetic progression (n+1)
Correlation: dot count = shape sides - 2 ✓

VERIFICATION:
- Figure 1: 3 sides, 1 dot (3-2=1) ✓
- Figure 2: 4 sides, 2 dots (4-2=2) ✓
- Figure 3: 5 sides, 3 dots (5-2=3) ✓
- Figure 4: 6 sides, 4 dots (6-2=4) ✓

APPLICATION:
Figure 5 should have:
- Outer: 6 + 1 = 7 sides (heptagon)
- Inner: 4 + 1 = 5 dots
- Verification: 7 - 2 = 5 ✓

ADVANCED NESTED RULE TECHNIQUES:
- Analyze each level independently
- Check for correlations between levels
- Verify consistency across all levels
- Apply all rules to predict next state
- Cross-verify using relationships

COMMON MISTAKES TO AVOID:
- Analyzing only one level
- Missing the relationship between levels
- Not verifying correlation formulas
- Applying only one rule to prediction
- Incomplete hierarchical decomposition

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

ABSTRACT RELATIONSHIP ANALYSIS:

Step 1: Analyze the relationship between Figure 1 and Figure 2
- Figure 1: Triangle
- Figure 2: 3 circles

Step 2: Identify properties of Figure 1
- Shape: Triangle
- Number of corners/vertices: 3
- Number of sides: 3

Step 3: Identify properties of Figure 2
- Shape: Circles
- Count: 3

RELATIONSHIP HYPOTHESIS:
The count of shapes in Figure 2 equals the number of corners in Figure 1

Step 4: Formulate the rule
Rule: "The second figure in each pair contains as many shapes as the first figure has corners"

VERIFICATION:
- Figure 1: Triangle has 3 corners
- Figure 2: Shows 3 circles ✓
- Relationship confirmed!

APPLICATION TO NEW PAIR:
- Figure 3: Square has 4 corners
- Figure 4 should: Show 4 shapes (circles)

ABSTRACT REASONING PRINCIPLES:
- Look beyond geometric transformations
- Consider numerical relationships
- Examine property mappings (corners → count)
- Test hypothesis on known pairs
- Apply verified rule to new cases

RELATIONSHIP DETECTION STRATEGIES:
1. Identify all properties of source figure
2. Identify all properties of target figure
3. Look for numerical correspondences
4. Check property-to-property mappings
5. Formulate relationship rule
6. Verify on all given pairs
7. Apply to predict unknown

COMMON MISTAKES TO AVOID:
- Looking only for visual transformations
- Missing abstract numerical relationships
- Not considering shape properties (corners, sides, etc.)
- Assuming relationship must be geometric
- Not verifying hypothesis on all pairs

PATTERN ANALYSIS:
Step 1: Examine the fill/shading in each figure
Step 2: Look for systematic changes in shading

RULE HYPOTHESIS:
The shading pattern adds one more filled segment each time

VERIFICATION:
Check pattern consistency across all four figures ✓

APPLICATION:
Based on the identified rule, the next figure should continue the pattern

SHADING ANALYSIS TECHNIQUES:
- Check for binary patterns (filled/unfilled)
- Look for cyclic color patterns
- Count filled vs unfilled elements
- Observe progressive filling patterns
- Check for symmetry in shading

COMMON MISTAKES TO AVOID:
- Missing subtle shading differences
- Not recognizing cyclic patterns
- Assuming random shading changes
- Overlooking progressive patterns

PATTERN ANALYSIS:
Step 1: Track the position of the dot in each figure
- Figure 1: Position at (40, 60)
- Figure 2: Position at (60, 40)
- Figure 3: Position at (80, 60)
- Figure 4: Position at (60, 80)

Step 2: Analyze movement vectors
- Fig 1→2: Δx = 20, Δy = -20
- Fig 2→3: Δx = 20, Δy = 20
- Fig 3→4: Δx = -20, Δy = 20

Step 3: Detect movement pattern
The dot follows a spiral inward pattern

RULE HYPOTHESIS:
Systematic positional movement following spiral inward pattern

VERIFICATION:
All movements conform to the identified pattern ✓

APPLICATION:
Next position: (50, 60)
Following the established spiral inward pattern

ADVANCED TECHNIQUES:
- Plot positions on coordinate system
- Check for symmetry and periodicity
- Analyze velocity and acceleration vectors
- Consider boundary conditions

COMMON MISTAKES TO AVOID:
- Assuming simple linear movement
- Not considering boundary reflections
- Missing rotational or circular patterns
- Ignoring spatial constraints

HIERARCHICAL RULE DETECTION:

LEVEL 1 ANALYSIS - Outer Shape Pattern:
Step 1: Identify shapes by counting sides
- Figure 1: Triangle (3 sides)
- Figure 2: Square (4 sides)
- Figure 3: Pentagon (5 sides)
- Figure 4: Hexagon (6 sides)

Rule 1 (Outer): Shape gains +1 side per step

LEVEL 2 ANALYSIS - Inner Element Pattern:
Step 2: Count dots inside each shape
- Figure 1: 1 dot
- Figure 2: 2 dots
- Figure 3: 3 dots
- Figure 4: 4 dots

Rule 2 (Inner): Number of dots increases by +1 per step

NESTED RULE HYPOTHESIS:
TWO independent hierarchical rules:
1. Outer rule: Polygon sides = 3, 4, 5, 6, ...
2. Inner rule: Dot count = 1, 2, 3, 4, ...

CORRELATION CHECK:
Both patterns follow same arithmetic progression (n+1)
Correlation: dot count = shape sides - 2 ✓

VERIFICATION:
- Figure 1: 3 sides, 1 dot (3-2=1) ✓
- Figure 2: 4 sides, 2 dots (4-2=2) ✓
- Figure 3: 5 sides, 3 dots (5-2=3) ✓
- Figure 4: 6 sides, 4 dots (6-2=4) ✓

APPLICATION:
Figure 5 should have:
- Outer: 6 + 1 = 7 sides (heptagon)
- Inner: 4 + 1 = 5 dots
- Verification: 7 - 2 = 5 ✓

ADVANCED NESTED RULE TECHNIQUES:
- Analyze each level independently
- Check for correlations between levels
- Verify consistency across all levels
- Apply all rules to predict next state
- Cross-verify using relationships

COMMON MISTAKES TO AVOID:
- Analyzing only one level
- Missing the relationship between levels
- Not verifying correlation formulas
- Applying only one rule to prediction
- Incomplete hierarchical decomposition

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

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

PATTERN ANALYSIS:
Step 1: Examine the fill/shading in each figure
Step 2: Look for systematic changes in shading

RULE HYPOTHESIS:
The shading pattern adds one more filled segment each time

VERIFICATION:
Check pattern consistency across all four figures ✓

APPLICATION:
Based on the identified rule, the next figure should continue the pattern

SHADING ANALYSIS TECHNIQUES:
- Check for binary patterns (filled/unfilled)
- Look for cyclic color patterns
- Count filled vs unfilled elements
- Observe progressive filling patterns
- Check for symmetry in shading

COMMON MISTAKES TO AVOID:
- Missing subtle shading differences
- Not recognizing cyclic patterns
- Assuming random shading changes
- Overlooking progressive patterns

CONDITIONAL RULE ANALYSIS:

Step 1: Classify each figure
- Figure 1: Closed shape (circle) → has DOT inside
- Figure 2: Open shape (arc) → has LINE segment
- Figure 3: Closed shape (square) → has DOT inside
- Figure 4: Open shape (curve) → has LINE segment

Step 2: Identify the conditional pattern
Check correlation between shape type and marking:
- ALL closed shapes → contain dots ✓
- ALL open shapes → contain lines ✓

CONDITIONAL RULE HYPOTHESIS:
IF shape is CLOSED → THEN add dot inside
IF shape is OPEN → THEN add line segment

VERIFICATION:
Test hypothesis against all figures:
- Figure 1: Closed + Dot ✓
- Figure 2: Open + Line ✓
- Figure 3: Closed + Dot ✓
- Figure 4: Open + Line ✓

Rule verified across all cases ✓

APPLICATION:
Given: Next shape is a CLOSED triangle
Apply rule: IF closed → THEN add dot
Result: Triangle with dot inside

BOOLEAN LOGIC FRAMEWORK:
- Condition: IsClosed(shape)
- True branch: AddDot()
- False branch: AddLine()

CONDITIONAL RULE DETECTION STRATEGY:
1. Identify potential condition variables
2. Classify all examples by condition
3. Check for consistent outcomes per condition
4. Formulate IF-THEN rule
5. Verify rule on all examples
6. Apply to new case based on its condition

COMMON MISTAKES TO AVOID:
- Not recognizing the conditional nature
- Treating as simple alternating pattern
- Ignoring the shape property (open/closed)
- Applying wrong transformation for given condition
- Missing the IF-THEN logical structure

PATTERN ANALYSIS:
Step 1: Examine Figure 1 and Figure 2 - note the orientation change
Step 2: Check if rotation: No consistent rotation angle found
Step 3: Check for reflection: Yes! Figure 2 is a mirror image of Figure 1
Step 4: Identify reflection axis: vertical axis
Step 5: Verify pattern: Figure 3 is reflection of Figure 2 (back to original orientation)

RULE HYPOTHESIS:
The figures alternate between original and reflected across vertical axis

VERIFICATION:
- Figure 1: Original position
- Figure 2: Reflected across vertical axis ✓
- Figure 3: Reflected back to original ✓

APPLICATION:
Figure 4 should be reflected version (same as Figure 2)
Pattern: Original → Reflected → Original → Reflected

COMMON MISTAKES TO AVOID:
- Confusing reflection with rotation
- Identifying wrong axis of reflection
- Not recognizing alternating pattern