Valid “If….then” logical statements can be combined. Take these two:
Calicos are cats. If something is a cat, then it has a tail.
We get Ca* –> C and C –> T. They can be combined using the common variable:
Ca –> C –> T. We can also simply conclude Ca –> T (Calicos have tails)**. This becomes extremely important.
Make Sure Things Match
“Fish live only in water. Fish have gills.” You can’t combine those to form a longer chain.
F –> W and F –> G
You can only combine from necessary to sufficient, not sufficient to sufficient.
Next: Errors of necessary and sufficient conditions
*Notice that I stick to one variable as much as possible in diagrams. Two, max. Too often I see students draw things like CTW –> PBHRX –> No SPALHG. ….?!?!? Keep it simple, and focus on what’s important.
**Technically, this process of drawing a conclusion from two validly combined statements is called a “syllogism”. I will never use that word again; you don’t need to know it to do well on the LSAT.