45 LR Two Question 22
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Hi Dave,
How did you get J→not R?
I got few J→R because they said that "few classical jazz recording are played on the radio" and not "all jazz recording are not played on the radio" if there is still a few, then isn't that still 'some still played' and not 'all are not played'?
Yes! You're totally correct!
Here, I've acted as though I seem to think "few" means the same thing as "none."
And you're also correct in saying that those phrases are different. And you're also right to say that that difference is important.
So let me explain myself:
My use of conditional symbols for statements that aren't actually conditional is a kind of approximation.
Like this:
Imagine a multiple-choice math question that asked you for the product of pi and 13.
I know that pi is basically 3, so I can estimate the answer before I have to use my calculator to do any actual math. So, here, I would begin my assessment of answer choices by seeking an option that says 40 (give or take).
Now, pi is not 3. It's similar to 3, but it is absolutely different in a real and important way. Nevertheless, I may find great utility in beginning my approach with some approximation.
To continue the metaphor, imagine that the answers are:
(A) 22
(B) 27.5
(C) 31.45
(D) 40.84
(E) 49
I've got the right answer, even though I did so using a value that's inherently, really different from pi - and I did it fast.
Of course, what if the answers look like this?
(A) 39.85
(B) 40.15
(C) 40.45
(D) 40.84
(E) 41.84
In this instance, obviously, my approximation does me no good at all, and I'm going to have to be more precise in my calculations.
Questions in the LR are just like this.
I think it's appropriate and useful to begin our approach to a particular question by making use of estimation and approximation when we can (because estimates are often faster, simpler, and easier to perform than actual calculations), but that we must be prepared for the possibility that our estimation may prove insufficient for answers.
When that happens, we tighten up our calculations.
Make sense?