Conditional Diagrams & Contrapositives

[dinoram]

When attempting to diagram the following:
"We can't go to the park until we find a car to drive."

My answer was:
go to park -----> find car
CANNOT find car -----> DID NOT go to park

This is due to that rule I learned that about how the words unless, until, except and without are necessary condition indicators however the rest of the term (the sufficient condition) becomes negated.

But the answer was:
DID NOT find car -----> CANNOT go to park
go to park -----> find car

Does the rule not apply here? If so, why not? Or am I misunderstanding the conditional statement?

[BethRibet]

Hi Dinoram,

Your answer is fine -- the two answers are virtually the same, as in this case there's no functional difference between cannot and did not.

For the purposes of solving any given problem, if the logic is correct, that's what's critical -- if someone else starts with the contrapositive of what you started with, but you both wind up with the same statements, it will still work.

That is, you can have:

A --> B
and contrapositive: ~B--> ~A

and if someone else started with:
~B --> ~A
and then got your original condition by diagramming the contrapositive, there's no real problem.

Hope this helps!
Beth