course MTH 151
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wԓŝާ̑{xyf Student Name: assignment #002
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22:43:44 Note that there are 2 questions in this assignment. `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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RESPONSE --> I could not get the picture to appear but according to my sketch, region I contains letters a,c,f region II contains letters b,d,e region III contains letters g,k and there are no letters in region IV
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22:44:21 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.
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RESPONSE --> right
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22:52:30 `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? How many people are included in both circles? How many of the 35 people are not included in either circle?
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RESPONSE --> I am assuming the number 8 is divided evenly between the two groups to make it easier. So, I have 16 people in region II, 11 people in region III, and 8 people in region I. 16+11+8 = 35 people, therefore, there wouldn't be anyone who wasn't included in both circles and their overlap.
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22:56:37 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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RESPONSE --> I see. I didn't have to divide the number between the groups. I thought since there were 35 people in the room then all 35 must be represented within the circles.
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