Examkin

Question

Difficulty: MediumAssumptions in Conditional Logic

The city will implement the proposed congestion charge only if the public transit system's capacity is increased by at least 20 percent. Furthermore, the transit system's capacity can be expanded by that amount only if the state legislature approves the pending transit grant. Therefore, unless the state legislature approves the transit grant, the city's downtown air quality will not improve significantly.

The conclusion drawn above depends on which one of the following assumptions?

  1. The city's downtown air quality will improve significantly only if the proposed congestion charge is implemented.Answer
  2. B
    If the city implements the proposed congestion charge, the downtown air quality will improve significantly.
  3. C
    The state legislature's approval of the transit grant ensures that the public transit system's capacity will increase by at least 20 percent.
  4. D
    If the state legislature approves the transit grant, the city's downtown air quality will improve significantly.
  5. E
    The state legislature will not approve the transit grant unless the funds are specifically designated for reducing downtown air pollution.

Answer

The assumption that the city's downtown air quality will improve significantly only if the proposed congestion charge is implemented.
The argument requires a bridge between the failure to implement the congestion charge and the failure of air quality to improve. The premises prove that without the state grant, the congestion charge cannot be implemented. The conclusion states that without the state grant, air quality will not improve. For this to be true, the argument must assume that without the congestion charge, air quality will not improve. This translates logically to 'Air quality improves ONLY IF the congestion charge is implemented.'

Step-by-Step Solution

1
Diagram the conditional premises provided in the argument.
Premise 1: Implement Congestion Charge → Increase Transit Capacity. Premise 2: Increase Transit Capacity → State Grant Approved.
Mapping the explicit conditional statements is the first step in identifying logical gaps.
2
Combine the premises into a logical chain and find its contrapositive.
Chain: Implement Charge → Increase Capacity → State Grant Approved. Contrapositive: NOT State Grant Approved → NOT Increase Capacity → NOT Implement Charge.
Chaining the premises reveals the full scope of what is guaranteed when certain conditions are met or fail to be met.
3
Diagram the conclusion and compare it to the premise chain.
Conclusion: NOT State Grant Approved → NOT Air Quality Improve. We currently only have: NOT State Grant Approved → NOT Implement Charge.
Comparing what we have (premises) to what we need (conclusion) isolates the exact missing link.
4
Identify the missing conditional link (the assumption) that bridges the gap.
To get to 'NOT Air Quality Improve', we must assume: NOT Implement Charge → NOT Air Quality Improve. The contrapositive of this is: Air Quality Improve → Implement Charge (Air quality improves ONLY IF charge is implemented).
A valid argument must connect its premises to its conclusion without logical gaps.

Key Concept

Identifying necessary assumptions in conditional logic chains by diagramming premises, finding their contrapositives, and bridging the gap to the conclusion.
Rate this question

Topics

Assumptions in Conditional Logic

More questions from this topic