All ambulances are life savers. No ambulances are bumper cars. Then..."
All ambulances are life savers. (ambulances = life savers)
No ambulances are bumper cars (no ambulances = bumper cars)
But instead of "No bumper cars are life savers" and "No life savers are bumper cars" we are told that "Some life savers are no bumper cars" is the correct answer.
But if you turn the statements into equations (life savers replaces ambulances) this makes no sense. "All life savers are no bumper cars" would also be another way to render it. How did we go from "All" to "some"?
In terms of formal logic "Not All" = "Some Not", "Not all of the marbles are green" = "Some of the marbles are not green"
So "Some life savers are no bumper cars" could also be rendered as "Not all life savers are bumper cars" (NOT "All life savers are no bumper cars", that is something we don't know).
To take the real world terms out of it:
All
A are
L (this does NOT mean "All
L are
A" that is a totally different statement)
No
A are
B
Therefore:
Some
L are not
B
There could be all sorts of things in
L but we know at least some of them are not
B (cause they're
A)
The other two answers are wrong because:
"No
B are
L"
We know
L contains all of
A, but it could also contain a bunch of other things, some of which might be
B
"No
L are
B"
We know
A can't be
B, but again there could be a bunch of other things in
L some of which could be
B
To substitute other values in
A = "dogs",
B = "cats", and
L = "animals"
All dogs are animals (but not all animals are necessarily dogs)
No dogs are cats
Therefore some animals are not cats (cause they're dogs)
Where as "No cats are animals" and "No animals are cats" make no sense right?
I know it's weird to think "Some bumper cars could be life savers" cause it doesn't match up with real world logic, but in terms of formal logic it's more about the fact that with the two statements we were give we do not have enough information to prove otherwise.
"Some life savers are no bumper cars" is the only answer we can actually prove.
