1951 AMC 12 Problem 14
Attempt Problem 14 of the 1951 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1951 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
14.
In connection with proof in geometry, indicate which one of the following statements is incorrect:
Some statements are accepted without being proved.
In some instances there is more than one correct order in
proving certain propositions.
Every term used in a proof must have been
defined previously.
It is not possible to arrive by correct reasoning at a true
conclusion if, in the given, there is an untrue proposition.
Indirect proof can be used whenever there are two or more
contrary propositions.
Answer: C
Small hint:
Distinguish undefined primitive terms from unproved axioms
Big hint:
An axiomatic system cannot define every term without an infinite regress
Solution:
An axiomatic development begins with primitive terms that are deliberately left undefined, as well as statements accepted without proof. Therefore it is not true that every term in a proof must previously have been defined.
Thus, the intended correct answer is C.
Problem 14 in other years
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