by ohthatpatrick Tue May 09, 2017 2:38 pm
This one said
"If W is after P, R will be after T"
We could symbolize that as
P -- W --> T -- R
Any time we have a conditional,
1 --> 2
we write the contrapositive, which is
-2 --> -1
So we need to write
- (T -- R) ---> - (P -- W)
However, with ordering rules like this, there's an easier way to think about saying
- (T -- R)
After all, that is saying "It is NOT the case that T is before R."
Okay, well then where IS it?
It must be that T is after R. Those are our only two choices.
Negating an ordering relationship basically gives you the opposite ordering relationship
- (T -- R) = R -- T
So instead of writing
- (T -- R) ---> - (P -- W)
we could write
R -- T ---> W -- P
==== looking at your mistake =====
The original was
P -- W --> T -- R
and you said we could infer
P -- W ---> R -- T
That's a contradiction!
The same left side idea forces us to do two opposite right side ideas?