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Difference between revisions of "1953 AHSME Problems/Problem 40"

(Created page with "==Problem== The negation of the statement "all men are honest," is: <math>\textbf{(A)}\ \text{no men are honest} \qquad \textbf{(B)}\ \text{all men are dishonest} \\ \textbf...")
 
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==Solution==
 
==Solution==
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This statement can also be written as "If someone is a man, then they are honest."
 
  
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The negation of this statement is "If someone is a man, then they are not honest."
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Note that <math>\textbf{(A)}</math> and <math>\textbf{(B)}</math> are the same, and <math>\textbf{(D)}</math> is the same as the quote in the statement "all men are honest" (that we have to found its negation). If not all men are honest, then that means that there is at least 1 dishonest (could be just one that spoils it for all the rest, or 5, for one, we definitely can't say it's all of them who are dishonest). So: <math>\textbf{(C)}</math>.
  
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The statement that means the same as the statement above is <math>\boxed{\textbf{(B)} \text{all men are dishonest}}</math>
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==See Also==
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{{AHSME 50p box|year=1953|num-b=39|num-a=41}}
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{{MAA Notice}}

Latest revision as of 16:02, 1 July 2021

Problem

The negation of the statement "all men are honest," is:

$\textbf{(A)}\ \text{no men are honest} \qquad \textbf{(B)}\ \text{all men are dishonest} \\ \textbf{(C)}\ \text{some men are dishonest}\qquad \textbf{(D)}\ \text{no men are dishonest}\\ \textbf{(E)}\ \text{some men are honest}$

Solution

Note that $\textbf{(A)}$ and $\textbf{(B)}$ are the same, and $\textbf{(D)}$ is the same as the quote in the statement "all men are honest" (that we have to found its negation). If not all men are honest, then that means that there is at least 1 dishonest (could be just one that spoils it for all the rest, or 5, for one, we definitely can't say it's all of them who are dishonest). So: $\textbf{(C)}$.

See Also

1953 AHSC (Problems • Answer Key • Resources)
Preceded by
Problem 39 		Followed by
Problem 41
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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