Combining Logical Statements

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.

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