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Difficulty: HardApplying the Negation Technique

When evaluating arguments on the LSAT, determining whether an assumption is strictly necessary requires properly applying the Negation Technique. This involves identifying the precise logical contradictory of a candidate statement. Match each candidate assumption regarding workforce productivity on the left with its precise logical negation on the right.

  • Any systemic transition to a compressed four-day workweek will inherently precipitate a sustained increase in aggregate workforce productivity.At least one systemic transition to a compressed four-day workweek will fail to precipitate a sustained increase in aggregate workforce productivity.
  • Only a systemic transition to a compressed four-day workweek possesses the capacity to precipitate a sustained increase in aggregate workforce productivity.A sustained increase in aggregate workforce productivity could be precipitated by structural changes other than a systemic transition to a compressed four-day workweek.
  • Most systemic transitions to a compressed four-day workweek will precipitate a sustained increase in aggregate workforce productivity.Half or fewer of the systemic transitions to a compressed four-day workweek will precipitate a sustained increase in aggregate workforce productivity.
  • At least some systemic transitions to a compressed four-day workweek will precipitate a sustained increase in aggregate workforce productivity.No systemic transition to a compressed four-day workweek will precipitate a sustained increase in aggregate workforce productivity.

Answer

The correct pairings isolate the specific quantifiers ('Any', 'Only', 'Most', 'Some') and match them with their precise logical contradictories.
Applying the Negation Technique effectively requires understanding the mathematical boundaries of logical quantifiers. 'Any' (100%) is contradicted by 'Not All' (<100%). 'Only' establishes a mandatory necessary condition, which is logically negated by showing alternatives exist. 'Most' (>50%) is negated by its mathematical complement (≤50%). 'Some' (>0%) is negated by 'None' (0%).

Step-by-Step Solution

1
Analyze the quantifier in 'Any systemic transition...'
The statement asserts 'All X are Y'. The logical contradictory is 'At least one X is not Y', which matches the option stating 'At least one... will fail'.
Negating a universal statement requires showing it is not absolute, rather than proposing its polar opposite ('None').
2
Analyze the restrictive conditional 'Only a systemic transition...'
The statement asserts 'No non-X is Y'. The contradictory is 'At least one non-X is Y', which matches the option stating the outcome 'could be precipitated by structural changes other than' the transition.
The negation of a necessary condition demonstrates that the necessary requirement could be bypassed, meaning the result can be achieved through alternative means.
3
Analyze the majority quantifier in 'Most systemic transitions...'
The statement asserts 'More than 50% of X are Y'. The contradictory encompasses the remaining mathematical space: '50% or fewer', matching the 'Half or fewer' option.
A common logical flaw is negating 'Most' with 'None' or 'Some are not', but the true logical contradictory splits the 100% distribution precisely at the 50% threshold.
4
Analyze the existential quantifier in 'At least some systemic transitions...'
The statement asserts 'At least one X is Y' (1% to 100%). The contradictory must cover the remaining space (0%), which matches 'No systemic transition...'.
If it is false that 'some' (even one) exist, then it must logically follow that 'none' exist.

Key Concept

Logical Quantifier Negation
Estimated Time:2m 0s
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Topics

Applying the Negation Technique

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