Match each candidate necessary assumption on the left with its logically precise contradictory on the right. This strict formulation is essential for properly testing assumptions in formal arguments.
- All genetically modified crops require less water than traditional varieties.At least one genetically modified crop does not require less water than traditional varieties.
- If the central bank raises interest rates, inflation will stabilize.The central bank raises interest rates, yet inflation fails to stabilize.
- Most of the artifacts discovered at the excavation site date back to the Bronze Age.Half or fewer of the artifacts discovered at the excavation site date back to the Bronze Age.
- No local businesses will survive the economic downturn without government subsidies.At least one local business will survive the economic downturn without government subsidies.
- Some current medical treatments rely on compounds derived from endangered plants.No current medical treatments rely on compounds derived from endangered plants.
Answer
Each assumption is matched with its precise logical contradictory: 'All' with 'At least one not', 'If A then B' with 'A and not B', 'Most' with 'Half or fewer', 'No' with 'At least one', and 'Some' with 'None'.
Applying the Negation Technique correctly involves identifying the minimal condition necessary to make the original statement false. For quantifiers, 'All' negates to 'Not all' (at least one does not), 'None' negates to 'Some' (at least one does), 'Some' negates to 'None', and 'Most' (more than half) negates to 'Half or fewer'. For conditional statements (If A then B), the negation is that the sufficient condition (A) occurs without the necessary condition (B).
Step-by-Step Solution
Key Concept
The Negation Technique requires finding the exact logical contradictory of a statement. This means identifying the minimal claim required to make the original statement false, avoiding polar opposites (like negating 'All' to 'None') or mistaken conditional negations.