How to write out the logic that justifies this conclusion?

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ScottRiqui

Posts: 3637
Joined: Mon Nov 29, 2010 8:09 pm

How to write out the logic that justifies this conclusion?

I'm used to drawing a conclusion from symbolic logic when the rules make a nice "chain", but even though I think the following conclusion is valid, I don't get a chain when I draw out the logic. Is my conclusion flawed, is the symbolic logic incorrect, or should I not be expecting to be able to form a "chain" from the statements given?

"Everyone who participated in the field trip was a student. Some of the field trip participants got lost. Therefore, some students got lost."

FT -> S
FT some L
-----------
S some L

There's not a "chain" in the typical sense, but does the first rule allow me to simply replace FT with S in the second rule, giving me the conclusion?

KFV

Posts: 55
Joined: Mon Nov 26, 2012 8:10 am

Re: How to write out the logic that justifies this conclusion?

Yes, exactly.

FT -> S can really be broken down into two statements:

F=S
~S=~F

(the equal signs only work left to right of course)