An archaeologist studying Artifacts A–D is interested in whether Artifact C is older than Artifact A.

Phase 1: Owning the Dataset

Argument Analysis Table

Key Patterns Identified

• We have a finite set of 4 artifacts (A, B, C, D)
• We need to establish relative age relationships
• The goal is to prove C is older than A
• We can use transitive properties (if X > Y and Y > Z, then X > Z)

Phase 2: Question Analysis & Prethinking

Understanding Each Part

• Part 1 Focus: We need an assertion about Artifact A's age relative to another artifact
• Part 2 Focus: We need an assertion about Artifact C's age relative to another artifact
• Relationship: These two assertions must combine to prove \(\mathrm{C > A}\)

Valid Inference Generation

To prove \(\mathrm{C > A}\), we can:

1. Direct comparison: Not available in our answer choices
2. Indirect proof through B: If \(\mathrm{C > B}\) and \(\mathrm{B > A}\), then \(\mathrm{C > A}\)
3. Indirect proof through D: If \(\mathrm{C > D}\) and \(\mathrm{D > A}\), then \(\mathrm{C > A}\)

Phase 3: Answer Choice Evaluation

Column 1 Options (Assertions involving Artifact A):

Option 1: "Artifact A is older than Artifact B" (\(\mathrm{A > B}\))

• What it claims: A predates B chronologically
• For our goal: If \(\mathrm{A > B}\), and we know something about C and B, this might not help prove \(\mathrm{C > A}\)

Option 2: "Artifact A is older than Artifact D" (\(\mathrm{A > D}\))

• What it claims: A predates D chronologically
• For our goal: Combined with \(\mathrm{C > D}\) wouldn't prove \(\mathrm{C > A}\)

Option 3: "Artifact B is older than Artifact A" (\(\mathrm{B > A}\))

• What it claims: B predates A chronologically
• For our goal: If \(\mathrm{B > A}\), and we can show \(\mathrm{C > B}\), then \(\mathrm{C > A}\) ✓

Column 2 Options (Assertions involving Artifact C):

Option 5: "Artifact C is older than Artifact D" (\(\mathrm{C > D}\))

• What it claims: C predates D chronologically
• For our goal: Would need \(\mathrm{D > A}\) from Column 1, which isn't available

Option 6: "Artifact C is older than Artifact B" (\(\mathrm{C > B}\))

• What it claims: C predates B chronologically
• For our goal: Combined with \(\mathrm{B > A}\) would prove \(\mathrm{C > A}\) ✓

Answer Selection Process

1. Part 1 Selection: "Artifact B is older than Artifact A" - This gives us \(\mathrm{B > A}\)
2. Part 2 Selection: "Artifact C is older than Artifact B" - This gives us \(\mathrm{C > B}\)
3. Verification: \(\mathrm{C > B}\) and \(\mathrm{B > A}\) → \(\mathrm{C > A}\) ✓

The transitive property confirms our goal: Since C is older than B, and B is older than A, then C must be older than A.

Common Traps Avoided

• We didn't assume relationships not stated in our selected assertions
• We relied only on logical transitivity, not speculation
• Each assertion is meaningful on its own and together they form a complete proof