18.6.07

"holiday"

i really don't like this holiday fuckaround. everything in the whole of your average university shuts down, leaving people like me the only fuckers on campus - and in the case of yours truly, the only fucker on campus. it's bizarre - the cafes and shops close down, the labs are empty, professors and tutors stop checking their email, all the experiments you can usually earn a good few bob from stop running and you're left to sort shit on your own. i hate summer vacation.

this means two things: one, i can eat cornflakes in the lab, and two, i have a lot of time on my metal-filled little hands. (there's a half a cannula in my left hand where the NHS suck.) thus, i have time to show you cool shit like the contrapositive implication.

in propositional logic, the IMPLIES operator looks like this: -> . if P implies Q, the implication can only be false where P is true and Q is false. the contrapositive is the reverse and NOT of an implication; that is, where P->Q, the contrapositive is !Q->!P. interestingly, it always gives the same truth value as the original implication.

you can prove this with a truth table:

P Q P->Q Q->P !Q->!P
--------------------------------------
t t t t t
t f f t f
f t t f t
f f t t t

the rows for P->Q and !Q->!P are the same, so the contrapositive is the same as the implication. cool, huh? so the next time you see a nasty-looking thing like !Q->!P, you know you can simplify it to P->Q.

man, i really gotta get a hobby.

Lepht

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