Match each everyday argument to the formal logical description that most accurately represents its valid deductive structure.
- If a municipality increases its reliance on solar energy, its overall grid stability improves. Since the grid stability of Oakhaven has not improved, it must be the case that Oakhaven has not increased its reliance on solar energy.Concludes that a sufficient condition did not occur by establishing the failure of a condition necessary for it.
- The newly discovered manuscript was authored either by Shakespeare or by one of his contemporaries. Linguistic analysis definitively rules out all of Shakespeare's contemporaries as possible authors. Therefore, the manuscript was authored by Shakespeare.Affirms one alternative of a disjunction by establishing the falsity of the only other alternative.
- Any employee promoted to senior management is required to attend the annual leadership retreat. Furthermore, anyone required to attend the annual leadership retreat receives an increased travel stipend. Consequently, any employee promoted to senior management receives an increased travel stipend.Derives a new conditional relationship by linking the necessary condition of one rule to the sufficient condition of another.
- All migratory birds in this region rely on the coastal wetlands for nesting. The Blue Heron is a migratory bird in this region. Thus, the Blue Heron relies on the coastal wetlands for nesting.Applies a universal property of a defined group to a specific member identified as belonging to that group.
Answer
The correct pairings match each specific argument to its abstract logical structure: the solar energy argument is Modus Tollens, the manuscript argument is Disjunctive Syllogism, the employee argument is Chain Conditionals, and the bird argument is Universal Instantiation.
Each argument represents an archetype of formal deductive logic. The first argument denies a necessary condition to rule out a sufficient condition. The second eliminates one side of a disjunction to prove the other. The third chains two conditionals through a shared middle term. The fourth applies a categorical rule to a specific entity.
Step-by-Step Solution
Key Concept
Identifying Valid Deductive Structures