Difference between revisions of "1959 AHSME Problems/Problem 47"
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== Solution == | == Solution == | ||
| − | <math>\fbox{}</math> | + | |
| + | All that we know about the freshmen is that they are all human (by statement I), so we can not prove assertion (1). | ||
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| + | Because all students are human (by statement II) and some students think (by statement III), some humans think, which proves assertion (2). | ||
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| + | Again, concerning the freshmen, all we know is that they are human. Thus, we cannot prove assertion (3). | ||
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| + | Concerning those who are not students, all that we can say is that some freshmen or humans might not be students. This information is not sufficient to prove assertion (4). | ||
| + | |||
| + | Thus, because we can only prove assertion (2), our answer is <math>\fbox{\textbf{(A)}}</math>. | ||
== See also == | == See also == | ||
{{AHSME 50p box|year=1959|num-b=46|num-a=48}} | {{AHSME 50p box|year=1959|num-b=46|num-a=48}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
| + | [[Category:Logic Problems]] | ||
Latest revision as of 12:05, 22 July 2024
Problem
Assume that the following three statements are true: (I). All freshmen are human. (II). All students are human. (III). Some students think.
Given the following four statements:
Those which are logical consequences of I, II, and III are:
Solution
All that we know about the freshmen is that they are all human (by statement I), so we can not prove assertion (1).
Because all students are human (by statement II) and some students think (by statement III), some humans think, which proves assertion (2).
Again, concerning the freshmen, all we know is that they are human. Thus, we cannot prove assertion (3).
Concerning those who are not students, all that we can say is that some freshmen or humans might not be students. This information is not sufficient to prove assertion (4).
Thus, because we can only prove assertion (2), our answer is 
.
See also
| 1959 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 46 |
Followed by Problem 48 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
