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Reasoning and Argument
Quick questions on Necessary and sufficient conditions explained: H2 Knowledge and Inquiry
5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What are mapping onto conditionals?Show answer
The conditional "if A then B" encodes both notions at once. It says A is sufficient for B (A guarantees B) and, equivalently, that B is necessary for A (A cannot occur without B). So in any conditional, the antecedent is the sufficient condition and the consequent is the necessary condition. Phrases like "only if" reverse the surface order: "A only if B" means B is necessary for A, that is, "if A then B."
What are definitions as biconditionals?Show answer
A good definition states conditions that are jointly necessary and sufficient, captured by "if and only if." To define a triangle as a closed three-sided polygon is to claim that being a closed three-sided polygon is both necessary for being a triangle (nothing else counts) and sufficient (anything that is one is a triangle). Most definitional disputes in philosophy are about whether a proposed set of conditions is really necessary and sufficient, the very form the tripartite analysis of knowledge takes.
What is q1?Show answer
Give an example of a condition that is necessary but not sufficient, and one that is sufficient but not necessary. [6 marks]
What is q2?Show answer
Translate "you may enter only if you have a ticket" into an if-then statement and say which condition the ticket is. [6 marks]
What is q3?Show answer
Explain why a good definition must give conditions that are both necessary and sufficient. [8 marks]
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