Match each candidate assumption statement on the left with its precise logical negation on the right. Accurately formulating these negations is a crucial step when applying the Negation Technique to evaluate Necessary Assumption questions on the LSAT.
- Every successful candidate in the election received campaign donations.At least one successful candidate in the election did not receive campaign donations.
- Some of the newly discovered artifacts date back to the third century.None of the newly discovered artifacts date back to the third century.
- Implementing the new protocol is the only way to secure the network.The network can be secured without implementing the new protocol.
- Most of the board members will vote in favor of the merger.Half or fewer of the board members will vote in favor of the merger.
Answer
The correct pairings match each statement's quantifier with its mutually exclusive and exhaustive opposite: 'Every' matches with 'At least one... did not'; 'Some' matches with 'None'; 'the only way' matches with 'can be secured without'; and 'Most' matches with 'Half or fewer'.
To apply the Negation Technique accurately, one must find the exact logical opposite of a statement. The logical opposite of 'all/every' is 'not all' (at least one is not). The logical opposite of 'some' (at least one) is 'none' (zero). The logical opposite of a necessary condition ('the only way') is showing the outcome can happen without it. The logical opposite of 'most' (51% to 100%) is 'half or fewer' (0% to 50%).
Step-by-Step Solution
Key Concept
Applying the Negation Technique to Formal Logic Quantifiers