Converse: Mathematical Logic

Thanks to ApolloFly for hosting mono Monday.  This was an interesting theme.  From the moment I saw it, I pronounced it CON-verse and immediately thought in terms of mathematical logic.  It was another area of study I enjoyed because it was like solving intricate puzzles.  (Later, I realized it could also be con-VERSE, as in talking.)


In logic, the converse of an implicational statement is a result of reversing the two parts.  It's usually stated if  P->Q the converse is Q->P.  I demonstrated this in the blip as:
If Kleenex are tissues then tissues are Kleenex.  (Pop quiz: T or F?)

There's a categorical proposition which also uses a converse.  Rather than singling out two items as above, it refers to entire groups.  This would be if ALL S  are P  then ALL P  are S.   The second statement is the converse of the first.  You could demonstrate this by saying ALL frogs are green so ALL things green are frogs.

From both examples, you can see (hopefully) that the converse doesn't necessarily follow from the original statement.

Sorry to use another mathematical example as a mono Monday entry.  The blip itself isn't that hot, although it did take me forever to put together.  I hope it was at least a tad interesting.

Q: Why wasn’t the geometry teacher at school?

A: Because she sprained her angle!!