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Difference between revisions of "1965 AHSME Problems/Problem 17"

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== Solution ==
 
== Solution ==
  
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<math>\fbox{E}</math>
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The given statement tells us that the weather being not fair is the only thing that can cancel the picnic on Sunday. It does not say that the weather being not fair necessarily cancels the picnic, so choice (A) is out. If the weather is fair, however, nothing can stop  the picnic from happening, so choice <math>\fbox{\textbf{(E)}}</math> is correct. <math>\newline</math>
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Choice (B) is incorrect, because if the picnic is cancelled, then the weather ''must'' be unfair, because the weather is the only thing that can stop the picnic. <math>\newline</math>
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Choice (C) is incorrect, because it is the [[contrapositive]] of choice (A), so (A) and (C) are logically equivalent. <math>\newline</math>
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Choice (D) is incorrect, because the picnic ''must'' be held if foul weather is not there to prevent it.
  
 
==See Also==
 
==See Also==
 
{{AHSME 40p box|year=1965|num-b=16|num-a=18}}
 
{{AHSME 40p box|year=1965|num-b=16|num-a=18}}
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{{MAA Notice}}
  
 
[[Category:Logic Problems]]
 
[[Category:Logic Problems]]

Latest revision as of 16:58, 18 July 2024

Problem

Given the true statement: The picnic on Sunday will not be held only if the weather is not fair. We can then conclude that:

$\textbf{(A)}\ \text{If the picnic is held, Sunday's weather is undoubtedly fair.} \\ \textbf{(B) }\ \text{If the picnic is not held, Sunday's weather is possibly unfair.} \\ \textbf{(C) }\ \text{If it is not fair Sunday, the picnic will not be held.} \\ \textbf{(D) }\ \text{If it is fair Sunday, the picnic may be held.} \\ \textbf{(E) }\ \text{If it is fair Sunday, the picnic must be held.}$

Solution

The given statement tells us that the weather being not fair is the only thing that can cancel the picnic on Sunday. It does not say that the weather being not fair necessarily cancels the picnic, so choice (A) is out. If the weather is fair, however, nothing can stop the picnic from happening, so choice $\fbox{\textbf{(E)}}$ is correct. $\newline$ Choice (B) is incorrect, because if the picnic is cancelled, then the weather must be unfair, because the weather is the only thing that can stop the picnic. $\newline$ Choice (C) is incorrect, because it is the contrapositive of choice (A), so (A) and (C) are logically equivalent. $\newline$ Choice (D) is incorrect, because the picnic must be held if foul weather is not there to prevent it.

See Also

1965 AHSC (Problems • Answer Key • Resources)
Preceded by
Problem 16 		Followed by
Problem 18
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
All AHSME Problems and Solutions

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