Select the answer choice that correctly diagrams the following Sufficient & Necessary statement:Any recycling cen...
samromano111May 7, 2020
Question
Hello,
I’m not sure why but I can’t figure out why it wouldn’t be
not W -> not N
And why it is
Not N -> Not W
I am reading the explanation and I know it talks about the word “any” but it doesn’t say that newsprint recycling centers always also recycle wood? Or maybe I am reading it wrong.
Replies
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There are two logically equivalent ways to write exactly the same statement: the direct way and the contrapositive.
The original (or direct) way was given:
W --> N
The contrapositive is achieved by both reversing and negating the statement:
not N --> not W
Any other arrangement isn't equal.
BenMingovJune 27, 2020
Hi Sam, thanks for the question.
As @Brett kindly pointed out, this is simply the contrapositive of the original statement. This is achieved by reversing and negating the statement.
Thank you very much @Brett!
I hope this helps @Sam, please let us know if you have any other questions!
RobertJuly 15, 2020
I have gotten in the habit of answering these questions with the contrapositive, since that is always the answer on the "drills" I have completed thus far. Are there scenarios or indicators like "any" that would request the direct interpretation?
STACEYCOX43November 18, 2020
Same here!!
NataliaJanuary 24, 2023
How do you know when to give the direct answer or when to give the contrapositive?
Emil-KunkinJanuary 25, 2023
Hi, either can be correct. You will never see a case where both a statement and it's contrapositive are both answer choices.
JacobAugust 1, 2023
Why is it asking for the contrapositive when it does not directly diagram the provided sentence?
Emil-KunkinAugust 1, 2023
The contrapositive contains all the information in the sentence, and is logically equal to it. It does indeed feel weird, but an initial statement and it's contrapositive really are the same thing.
