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.