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Difficulty: EasyDiagramming Conditional Statements

Arrange the following conditional statements in the correct logical sequence to form an unbroken deductive chain, starting from the initial trigger 'the new software is installed' and ending with the final outcome 'the quarterly budget is exceeded'.

  1. 1Whenever the new software is installed, server downtime inevitably occurs.
  2. 2Server downtime occurring is sufficient to cause an increase in customer complaints.
  3. 3An increase in customer complaints requires that the IT department works overtime.
  4. 4The IT department works overtime only if the quarterly budget is exceeded.

Answer

The correct sequence connects each necessary condition to the next sufficient condition to form the chain: Software is installed -> Server downtime occurs -> Customer complaints increase -> IT department works overtime -> Quarterly budget is exceeded.
The correct sequence accurately translates all conditional indicators into a valid transitive chain. 'Whenever' introduces a sufficient condition (Software -> Downtime). 'Is sufficient to' introduces a sufficient condition (Downtime -> Complaints). 'Requires' introduces a necessary condition (Complaints -> Overtime). 'Only if' introduces a necessary condition (Overtime -> Budget). Connecting these end-to-end forms an unbroken logical path.

Step-by-Step Solution

1
Identify the starting trigger and the final outcome from the prompt.
Start: 'Software is installed'. End: 'Budget is exceeded'.
Establishing the endpoints of the deductive chain helps anchor the ordering process.
2
Translate each English statement into formal 'If -> Then' logic using the conditional indicators.
Link 1: Software -> Downtime. Link 2: Downtime -> Complaints. Link 3: Complaints -> Overtime. Link 4: Overtime -> Budget.
Translating indicators like 'whenever', 'sufficient', 'requires', and 'only if' reveals the underlying logical direction of each statement.
3
Connect the statements by matching the necessary condition (right side) of one to the sufficient condition (left side) of the next.
The chain perfectly aligns as: Software -> Downtime -> Complaints -> Overtime -> Budget.
A valid transitive deductive chain must link overlapping conditions in a continuous sequence without reversing any relationships.

Key Concept

Diagramming and linking conditional statements (Transitive Property)
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Topics

Diagramming Conditional Statements

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