6. Physicists assume that, in any given system, if there is no light, then it is dark; and it has to be one or the other. In physics, then, if a system is "not dark," what must it be?
7. Nguyen is choosing whether to listen to jazz or rock music. Assuming "jazz" and "rock" are contraries here, what are his options?
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He can listen to jazz only, or to rock only. 
He can listen to jazz only, to rock only, to both, or to neither.
8. Trying to remember the colors of a dress, Cathy has narrowed it down to two options: blue and green. She knows that if blue is correct, then green cannot be, and if green is correct, then blue cannot be. In this case, therefore, blue and green are:
9. According to a news report, the senator contradicted her former position when she said that a flat tax would benefit the middle class. What must her former position have been, to create a contradiction?
10. Contrary to Kim's expectations, the critical thinking class was completely full. Assuming this case is indeed one of "contraries," what might Kim's expectations have been?
6. Physicists assume that, in any given system, if there is no light, then it is dark; and it has to be one or the other. In physics, then, if a system is "not dark," what must it be?
You answered:
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Light
It must be light. As we saw in Question 5, light and dark here are contradictory, meaning that "light" is "not dark," and "dark" is "not light."
6. Physicists assume that, in any given system, if there is no light, then it is dark; and it has to be one or the other. In physics, then, if a system is "not dark," what must it be?
You answered:
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Light and Dark
As we saw in Question 5, light and dark here are contradictory, meaning that "light" is "not dark," and "dark" is "not light."
6. Physicists assume that, in any given system, if there is no light, then it is dark; and it has to be one or the other. In physics, then, if a system is "not dark," what must it be?
You answered:
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Neither
As we saw in Question 5, light and dark here are contradictory, meaning that "light" is "not dark," and "dark" is "not light."
7. Nguyen is choosing whether to listen to jazz or rock music. Assuming "jazz" and "rock" are contraries here, what are his options?
You answered:
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He can listen to jazz only, or to rock only.
Jazz or rock only (but not "both" or "neither") would be contradictory
7. Nguyen is choosing whether to listen to jazz or rock music. Assuming "jazz" and "rock" are contraries here, what are his options?
You answered:
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He can listen to jazz only, to rock only, or to neither.
In contraries, either or neither can be true, but not both. So either jazz, or rock, or neither would be contrary.
7. Nguyen is choosing whether to listen to jazz or rock music. Assuming "jazz" and "rock" are contraries here, what are his options?
You answered:
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He can listen to jazz only, to rock only, to both, or to neither.
Jazz or rock or both or neither would be an unrestricted choice.
8. Trying to remember the colors of a dress, Cathy has narrowed it down to two options: blue and green. She knows that if blue is correct, then green cannot be, and if green is correct, then blue cannot be. In this case, therefore, blue and green are:
You answered:
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contradictory only
All we know is that blue and green both cannot be true. Whether they both can be false is not clear. To put it another way, if blue is not correct, can we conclude that green is? If so, blue and green are contradictory. If not, they are contrary. But we are not given that information.
8. Trying to remember the colors of a dress, Cathy has narrowed it down to two options: blue and green. She knows that if blue is correct, then green cannot be, and if green is correct, then blue cannot be. In this case, therefore, blue and green are:
You answered:
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contrary only
All we know is that blue and green both cannot be true. Whether they both can be false is not clear. To put it another way, if blue is not correct, can we conclude that green is? If so, blue and green are contradictory. If not, they are contrary. But we are not given that information.
8. Trying to remember the colors of a dress, Cathy has narrowed it down to two options: blue and green. She knows that if blue is correct, then green cannot be, and if green is correct, then blue cannot be. In this case, therefore, blue and green are:
You answered:
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either contradictory or contrary
Either contradictory or contrary, because all we know is that blue and green both cannot be true. Whether they both can be false is not clear. To put it another way, if blue is not correct, can we conclude that green is? If so, blue and green are contradictory. If not, they are contrary. But we are not given that information.
9. According to a news report, the senator contradicted her former position when she said that a flat tax would benefit the middle class. What must her former position have been, to create a contradiction?
You answered:
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That a flat tax would benefit the wealthy.
Saying that it would benefit the rich and benefit the middle class is neither contradictory nor contrary because they both can be true. So these are just unrestricted choices.
9. According to a news report, the senator contradicted her former position when she said that a flat tax would benefit the middle class. What must her former position have been, to create a contradiction?
You answered:
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That a flat tax would not benefit anyone.
It would be only contrary if her position had been that it did not benefit anyone. Though these cannot both be true--that it benefits no one and that it benefits the middle class--they both can be false: it could benefit only the rich, for example.
9. According to a news report, the senator contradicted her former position when she said that a flat tax would benefit the middle class. What must her former position have been, to create a contradiction?
You answered:
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That a flat tax would benefit everyone.
Saying that it would benefit everyone and benefit the middle class is neither contradictory nor contrary. For example, since the middle class is part of "everyone," these both can be true. And if "everyone" does not benefit, they are both false. So these are just unrestricted choices.
9. According to a news report, the senator contradicted her former position when she said that a flat tax would benefit the middle class. What must her former position have been, to create a contradiction?
You answered:
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That a flat tax would not benefit the middle class.
Since contradictions follow the form, "A and not-A," this contradiction is "benefit the middle class" and "not benefit the middle class."
10. Contrary to Kim's expectations, the critical thinking class was completely full. Assuming this case is indeed one of "contraries," what might Kim's expectations have been?
You answered:
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The critical thinking class was not completely full.
"Completely full" and "not completely full" are contradictory, fitting the form of "A and not-A."
10. Contrary to Kim's expectations, the critical thinking class was completely full. Assuming this case is indeed one of "contraries," what might Kim's expectations have been?
You answered:
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The critical thinking class was popular.
And if a class is popular, it might also be "completely full" (both), so this is simply a choice.
10. Contrary to Kim's expectations, the critical thinking class was completely full. Assuming this case is indeed one of "contraries," what might Kim's expectations have been?
You answered:
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The critical thinking class was completely empty.
"Not completely full" would mean that there was at least one seat open. And there would be "at least one seat open" in a class that was completely empty, so that would be the contrary. Notice, therefore, that when we say things like "contrary to her expectations," we may not be using the word "contrary" accurately.
10. Contrary to Kim's expectations, the critical thinking class was completely full. Assuming this case is indeed one of "contraries," what might Kim's expectations have been?
You answered:
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The critical thinking class was not completely empty.
If something is not completely empty, it might be "completely full," which would make these both true; and "empty" would then be neither, so they are unrestricted choices.
Congratulations!
You have finished the exercises for the "Options" section.
