College Algebra: help with study guide (solution sets, etc)

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WrenMaria98

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The inequality is 5x-7y>-35

Set A is the boundary line
Set B is the half-plane containing the origin
Set C is the half-plane not containing the origin

1. If a point in set B is a solution to 5x-7y>-35 than B is the ___________ for 5x-7y>-35 (is this the solution set?)

2. If a point in set C is a solution to 5x-7y>-35 then C is the ___________ for 5x-7y>-35 (also the solution set?

3. If a point in set B is NOT a solution to 5x-7y>-35 then B is the solution set for __________ (is it 5x-7y < -35?)

4. If a point in set C is NOT a solution to 5x-7y>-35 then C is the solution set for _________ (5x-7y < -35?)

5. The set A is the solution set for _________ (5x-7= -35)

6. The set B is the solution set for _________ (5x-7y > -35?)

7. The set C is the solution set for _________ (5x-7y < -35?)

For the three sets A,B, and C the following are true:

8. A ? B ? C = ???

9. A ? B = ???

10. A ? C = ???

11. B ? C = ???

12. The above are true because of the ______ _____ ___________ (law of trichotomy??)
 
The inequality is 5x-7y>-35

Set A is the boundary line
Set B is the half-plane containing the origin
Set C is the half-plane not containing the origin

1. If a point in set B is a solution to 5x-7y>-35 than B is the ___________ for 5x-7y>-35 (is this the solution set?)

2. If a point in set C is a solution to 5x-7y>-35 then C is the ___________ for 5x-7y>-35 (also the solution set?

3. If a point in set B is NOT a solution to 5x-7y>-35 then B is the solution set for __________ (is it 5x-7y < -35?)

4. If a point in set C is NOT a solution to 5x-7y>-35 then C is the solution set for _________ (5x-7y < -35?)

5. The set A is the solution set for _________ (5x-7= -35)

6. The set B is the solution set for _________ (5x-7y > -35?)

7. The set C is the solution set for _________ (5x-7y < -35?)

For the three sets A,B, and C the following are true:

8. A ? B ? C = ???

9. A ? B = ???

10. A ? C = ???

11. B ? C = ???

12. The above are true because of the ______ _____ ___________ (law of trichotomy??)
Click to expand...

The first 7 appear to be correct, except on 3 and 4 where you need to add an equal sign to the inequality; i.e., they should read “less than or equal to.” That’s because you need to include the line as well as the half-plane in the answer.

For 8, I’d say the union of all three sets just means all possible points (x,y).

For 9, 10, and 11, I think they just want you to say that the intersections are the “null set” or “empty set” since all three sets are mutually exclusive.

I believe 12 is correct.

Hope that helps.
 
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