second open qa

course Mth151

If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

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Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

002. Representing Sets

`routine Venn1

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Question: `q001Note that there are 2 questions in this assignment.

There are two questions in this assignment

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Self-critique (if necessary):

Self-critique Rating:

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Question: `q001. We can represent the collection consisting of the letters a, b, c, d, e, f by a circle in which we write these letters. If we have another collection consisting of the letters a, c, f, g, k, we could represent it also by a circle containing these letters. If both collections are represented in the same diagram, then since the two collections have certain elements in common the two circles should overlap.

Sketch a diagram with two overlapping circles. The two circles will create four regions (click below on 'Next Picture'). The first region is the region where the circles overlap. The second region is the one outside of both circles. The third region is the part of the first circle that doesn't include the overlap. The fourth region is the part of the second circle that doesn't include the overlap. Number these regions with the Roman numerals I (the overlap), II (first circle outside overlap), III (second circle outside overlap) and IV (outside both circles).

Let the first circle contain the letters in the first collection and let the second circle contain the letters in the second collection, with the letters common to both circles represented in the overlapping region.

Which letters, if any, go in region I, which in region II, which in region III and which in region IV?

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Your solution:

A, c, f go in region 1 b,d,e go in region 2 and g and k go in region 3

Confidence Assessment:

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Given Solution:

The letters a, c and f go in the overlapping region, which we called Region I. The remaining letters in the first collection are b, d, and e, and they go in the part of the first circle that does not include the overlapping region, which we called Region II. The letters g and k go in the part of the second circle that does not include the overlapping region (Region III). There are no letters in Region IV.

Click below on 'Next Picture' for a picture.

`routine Venn2

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Self-critique (if necessary):

Self-critique Rating:

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Question: `q002. Suppose that we have a total of 35 people in a room. Of these, 20 have dark hair and 15 have bright eyes. There are 8 people with dark hair and bright eyes.

Draw two circles, one representing the dark-haired people and the other representing the bright-eyed people. Represent the dark-haired people without bright eyes by writing this number in the part of the first circle that doesn't include the overlap (region II). Represent the number of bright-eyed people without dark hair by writing this number in the part of the second circle that doesn't include the overlap (region III). Write the appropriate number in the overlap (region I).

How many people are included in the first circle, and how many in the second? 20-8=12 and 15-8=7

How many people are included in both circles? 19+8 that have both bright eyes and dark hair equals 27

How many of the 35 people are not included in either circle? 8 people are not included in the circle

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Your solution:

Confidence Assessment:

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Given Solution:

Of the 20 dark-haired people in the preceding example, 8 also have bright eyes. This leaves 12 dark-haired people for that part of the circle that doesn't include the overlap (region I).

The 8 having both dark hair and bright eyes will occupy the overlap (region I).

Of the 15 people with bright eyes, 8 also have dark hair so the other 7 do not have dark hair, and this number will be represented by the part of the second circle that doesn't include the overlap (region III).

We have accounted for 12 + 8 + 7 = 27 people. This leaves 35-27 = 8 people who are not included in either of the circles. The number 8 can be written outside the two circles (region IV) to indicate the 8 people who have neither dark hair nor bright eyes (click below on 'Next Picture').

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Self-critique (if necessary):

Self-critique Rating:

&#When you do not answer a question you need to continue in your self-critique with a phrase-by-phrase analysis of the solution, detailing everything you do and do not understand. Specific questions are encouraged if you do not understand everything.

You should of course always attempt a solution and detail your thinking about what the problem means and how you might solve it. Even an incorrect attempt forms a basis for correction and subsequent understanding.

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&#Good work. See my notes and let me know if you have questions. &#