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Understanding Opposites

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I understand the concept of Global and local questions. The global questions encompass the overall rules of the game, and the local questions add a new condition to the game that only applies to that one question. What I am having trouble with is the idea of logical and polar opposites. Also the idea of converting answers with the work EXCEPT into terms of truth. I got all the exercises wrong on pages 137-139. In looking at number 2 on page 137 if something could be true EXCEPT, I would think the correct answer is not necessarily true and the four incorrect answers are could be true. With number 3 on page 137 I would think the correct answer could be false, and the four incorrect answers must be true. That would be wrong. I am getting discouraged about this. :cry: :cry: :cry: :cry: Any help with trying to understand this is greatly greatly appreciated.

Dave Killoran
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Hi LawLover,

Thanks for the question! You are closer here than you think :-D

First, the following are ALWAYS paired as opposites (in either order; these are pairs and whichever is "first" doesn't matter):

    Must vs Not Necessarily

    Could vs Cannot

So, if you lock on to one of those ideas, the opposite will always be the other half of the pair. Let's revisit #3 then with that in mind (with some helpful italics):

    If K is displayed third, then each of the following could be true EXCEPT:

    Ok, you correctly identified that the 4 wrong answers are Could Be True. So, what's the opposite idea in that pair? Cannot. and so we have the following:

    Incorrect Answers: Could Be True

    Correct Answer: Cannot Be True

You ran into problems because you paired Could vs Not Necessarily, which never happens when we are looking for opposites.

With #3, we know “could be false” is equivalent to “not necessarily true.” So, our correct answer is Not Necessarily True. what's idea paired with Not Necessarily? Must, and so we have the following:

    Correct Answer: Not Necessarily True

    Four Incorrect Answers: Must Be True

If I could make a guess, I'd say you have mixed up the opposite conversions with the false-to-true conversions. Opposites are always the following:

    Must vs Not Necessarily

    Could vs Cannot

But the False-to-True Conversions look like this:

    Must :dbl: Cannot

    Could :dbl: Not Necessarily

So, if you saw a Must Be False question that translates to Cannot Be True. And, Cannot Be False translates to Must Be True. Same for the bottom pair.

Tricky at first, but you are already pretty close. If you can make the adjustment and memorize the pairings above, after a while this turns into second nature (kind of like how learning to drive a stick-shift car is tough at first, but then eventually people do it without even thinking).

Keep working on this—you'll have it soon!
Dave Killoran
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