A plumbing contractor is scheduling plumbers on her crew to work at five job sites next week - an apartment...

Solution: Two-Part Analysis - Plumbing Contractor Scheduling

Visual Representation

Job Sites:

• A: Apartment complex
• D: Department store
• O: Office building
• R: Restaurant
• S: School

Requirements (as logical statements):

1. \(\mathrm{A} \to (\mathrm{D} \lor \mathrm{S})\): If plumber works on A, then must work on D or S
2. \(\mathrm{R} \to \mathrm{O}\): If plumber works on R, then must work on O
3. \((\mathrm{R} \land \neg\mathrm{S}) \to \mathrm{D}\): If plumber works on R but not S, then must work on D
4. \((\mathrm{D} \land \mathrm{S}) \to \mathrm{O}\): If plumber works on both D and S, then must work on O

Understanding the Question

We need to find two job sites that complete: "Any plumber working on the [1] must also work on the [2]"

This statement has the form: \(\mathrm{X} \to \mathrm{Y}\) (If X then Y)

Processing the Solution

Analyzing Each Requirement

Requirement 1: \(\mathrm{A} \to (\mathrm{D} \lor \mathrm{S})\)
- Cannot be expressed as simple "\(\mathrm{X} \to \mathrm{Y}\)" because conclusion has OR condition
- Would need: "Any plumber working on A must work on D or S"

Requirement 2: \(\mathrm{R} \to \mathrm{O}\)
- Perfect match!
- Can be expressed as: "Any plumber working on R must also work on O"
- This is exactly the format requested

Requirement 3: \((\mathrm{R} \land \neg\mathrm{S}) \to \mathrm{D}\)
- Cannot fit because premise has compound condition
- Would need: "Any plumber working on R but not on S must work on D"

Requirement 4: \((\mathrm{D} \land \mathrm{S}) \to \mathrm{O}\)
- Cannot fit because premise requires working on BOTH sites
- Would need: "Any plumber working on both D and S must work on O"

Critical Insight

Only Requirement 2 can be expressed in the simple "If X then Y" format without additional conditions or qualifiers.

Final Solution

Answer:
- Column 1: restaurant
- Column 2: office building

Verification: "Any plumber working on the restaurant must also work on the office building" accurately reexpresses Requirement 2.

Key Exam Strategy

When asked to reexpress requirements:

1. First convert all requirements to logical notation
2. Identify which can fit the requested format without modification
3. Requirements with OR conditions, NOT conditions, or AND conditions in the premise typically cannot be simplified to basic "If X then Y" statements