# We’re Not Just Sure, We’re Contrapositive

So I lied.  One more basics post.

We’ve dealt so far with how to conceptualize and diagram conditional statements.  Here are two special cases that come up from time to time:

No – The word no is just as logically strong as all and when, and also indicates a form of sufficiency.  Let’s say we take a break from shooting the most expensive music video ever [1] to fight Krist Novoselic backstage [2] and for some reason play a dueling-pianos duet with Sir Elton:

Why do we do it?  Because nothing lasts forever, even cold November rain.  More precisely, no thing lasts forever.

How do we deal with a statement like that?  Two steps:

1.  Change the no to an all.

All things last forever, or, if it’s a thing, then it lasts forever.

T –> F

2.  Negate the necessary condition.

If it’s a thing, then it does not last forever.

T –> /F

So, no thing lasts forever becomes

T –> /F.

AND/OR contrapositives

Sometimes, you can get conditionals with conjunctions [ANDs] or disjunctions [ORs] in them.  Like this:

What does Gene Simmons do on an average night?  Two things.  He rocks and he rolls.  If it’s night, he’s rocking and rolling. [4]

N –> Rock and Roll

The contrapositive of this needs a slight tweak.  Since we know night is enough to guarantee that we both rock and roll, the absence of one or the other means it can’t be night.

/Rock or /Roll –> /N

Simple lesson: when taking a contrapositive, just switch and to or and vice versa.

Homework example:

So ladies if the butt is round

And you wanna triple-X-throw down

Dial 1-900-MIX-A-LOT.

Kick them nasty thoughts.  Baby got back. [5]

[1] November Rain was the most expensive music video ever shot at the time, mostly due to the rotating helicopter shot of Slash outside the church.  It was eclipsed almost immediately in cost by TLC’s Waterfalls.

[2] Guns N’ Roses got into an infamous backstage scuffle with Nirvana at either the 1991 or 1992 MTV Music Video Awards.  I’m too amazed Slash is relatively sober enough to play the solos on the beat [3] to remember.

[3] Scratch that.  I just heard the outro solo.

[4] We’ll ignore for now how he also parties ev-e-ry day.

[5] Trivia time: the masterful introduction to Baby Got Back was done, in a woefully uncredited role, by Mrs. Mix-A-Lot.