course Mth 151 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.
.............................................
Given Solution: The circles would appear and be labeled as below: 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. Self-critique (if necessary): OK Self-critique Rating: OK ********************************************* 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? First circle: 12 Second circle: 7 How many people are included in both circles? Both circles: 8 How many of the 35 people are not included in either circle? 12+8+7= 27 35-27= 8 8 people are not included in the circle. Your solution: Confidence Assessment: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.............................................
Given Solution: These numbers are represented in the circles below. • A number on the boundary of a circle indicates the total number in that circle, so the figure represents 20 individuals in circle A and 15 in circle B. The number 35 on the boundary of the entire figure represents the total number of individuals in the room, which in this case is 35. • A number inside one of the regions I, II, III, IV represents the number in that region. The 8 having both dark hair and bright eyes will occupy the overlap between the circles (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). This is indicated by the number 7 inside region III in the figure below. 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 II). 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, as is indicated by the number 8 in region IV in the figure below: &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): Self-critique Rating "