Here I will prove that the paradigm "People in cars cause
accidents,accidents in cars cause people" is not equivalent to a
bi-conditional operator.
Define the following events:... See More
A = People
B = Car (location)
C = Accident occurs
Therefore,
A & B is denoted as the subject is a person and is in a car. Agreed.
Therefore,
we designate the next event as an embedment to the former, which
corresponds to "people in cars cause accidents," namely:
1.) (A & B ) -> C
Then we define our second statement, "accidents in cars cause people" as follows:
2.) (C & B) -> A
Remember
the converse error, if the subject is not a person (unlikely) and is
not in a car, rather (A & B ) = false, then an accident cannot
occur.
You can use DeMorgan's law to confirm this as follows:
!(A & B) = !A || !B (remember that the OR is inclusive!)
So, lets get back to the topic now that we have the terminology out of the way.
((A & B)-> C) <--> ((C & B) -> A)
and
((A & B)-> C) --> ((C & B) -> A)
Where
the second statement is valid (because If (if the subject is a person,
and is in a car, then accidents arise) then (accidents arise in cars if
the subject is a person). Sigh, there is more to this, but I'm lazy and
have no time to show why this is valid.