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Mathematics 15 Online
OpenStudy (anonymous):

Use Euler circles to check the validity of the argument. All scientists are eccentrics. All eccentrics are kind. Therefore, all scientists are kind. How do I find out if this is valid or not?

jimthompson5910 (jim_thompson5910):

Here is a circle to represent the set of all kind people |dw:1403394483554:dw|

jimthompson5910 (jim_thompson5910):

Inside it, draw another circle to represent the set of eccentric people. This new circle is completely contained in the previous one because "All eccentrics are kind" |dw:1403394589095:dw|

jimthompson5910 (jim_thompson5910):

then draw another circle inside the one we just drew to represent the set of scientists this is completely contained in the eccentric circle because " All scientists are eccentrics" |dw:1403394645925:dw|

jimthompson5910 (jim_thompson5910):

so we can see that "Therefore, all scientists are kind. " is a true statement because every scientist is also in the "kind people" circle

OpenStudy (anonymous):

ohhhh

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