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Difference between revisions of "1951 AHSME Problems/Problem 14"

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== Problem ==
 
== Problem ==
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In connection with proof in geometry, indicate which one of the following statements is [i]incorrect[/i]:
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In connection with proof in geometry, indicate which one of the following statements is ''incorrect'':
  
 
<math> \textbf{(A)}\ \text{Some statements are accepted without being proved.}</math>
 
<math> \textbf{(A)}\ \text{Some statements are accepted without being proved.}</math>
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== Solution ==  
 
== Solution ==  
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{{solution}}
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After reading the options, it is very apparent that <math> \textbf{(E)}\ \text{Indirect proof can be used whenever there are two or more contrary propositions.}</math> is the correct answer; rigorous proof is needed no matter what.
  
 
== See Also ==
 
== See Also ==
 
{{AHSME 50p box|year=1951|num-b=13|num-a=15}}
 
{{AHSME 50p box|year=1951|num-b=13|num-a=15}}
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{{MAA Notice}}

Latest revision as of 11:20, 5 July 2013

Problem

In connection with proof in geometry, indicate which one of the following statements is incorrect:

$\textbf{(A)}\ \text{Some statements are accepted without being proved.}$ $\textbf{(B)}\ \text{In some instances there is more than one correct order in proving certain propositions.}$ $\textbf{(C)}\ \text{Every term used in a proof must have been defined previously.}$ $\textbf{(D)}\ \text{It is not possible to arrive by correct reasoning at a true conclusion if, in the given, there is an untrue proposition.}$ $\textbf{(E)}\ \text{Indirect proof can be used whenever there are two or more contrary propositions.}$

Solution

After reading the options, it is very apparent that $\textbf{(E)}\ \text{Indirect proof can be used whenever there are two or more contrary propositions.}$ is the correct answer; rigorous proof is needed no matter what.

See Also

1951 AHSC (Problems • Answer Key • Resources)
Preceded by
Problem 13 		Followed by
Problem 15
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50
All AHSME Problems and Solutions

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