Question 1199145
Use one of the 3 methods of syllogistic logic to determine whether the following syllogism is 
valid:
No carrots are red fruits.<pre>[Translation: if we have something that fits the category of being a carrot, then
it does not fit both the category of being red and the category of being a fruit.]

C ⊃ ~(R • F)</pre>Some fruits are carrots.<pre>[Translation: We DO have some things that fit the category of being a fruit and
the category of being a carrot.

F • C</pre>Therefore, some fruits are not red fruits.<pre>[Translation: We DO have some things that fit the category of being a fruit but (and) 
do not fit the category of being red.]

F • ~R

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1.  C ⊃ ~(R • F)
2.  F • C                 / F  • ~R
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3.  F        2, simplification
4.  C • F    2, commutation
5.  C        4, simplification
6.  ~(R • F) 1,5 modus ponens
7.  ~R v ~F  6, DeMorgan's law 
8.  ~F v ~R  7, commutation
9.  ~~F      3, double negation
10. ~R       8,9, disjunctive syllogism
11. F • ~R   3,10 conjunction

The conclusion has been reached. This shows that the argument is valid.

Edwin</pre>