Here is an example of a Venn diagram with three sets. Example 8: In a survey, adults Travel Options Frequency were asked how they travel to Just Car 157 work. Below is the recorded data Just Bike 20 on how many people bused, Just Bus 35 Car and Bike only 35 biked, and/or drove to work. Car and Bus only 10 Draw and label a Venn diagram Bus and Bike only 8 using the information in the Car, Bus and Bike 12 table. Neither Car, Bus nor Bike 15 292 To fill in the Venn diagram, we will place the 157 people who only drive a car in the car set where it does not overlap with any other modes of transportation. We can fill in the numbers 20 and 35 in a similar way. Then we have the overlap of two use all three modes, so they are modes of transportation only. in the intersection of all three There are 35 people who use sets. There are 15 people who do their car and bike only, so they not use any of the three modes, go in the overlap of those two so they are placed outside the sets, but they do not take the bus, circles but inside the universal so they are outside of the bus set. set of all modes of Similarly, we can enter the 10 transportation. Here is the and 8. There are 12 people who completed Venn diagram. Example 9: One hundred fifty people were surveyed and asked if they believed in UFOs, ghosts, and Bigfoot. The following results were recorded. 43 believed in UFOs 44 believed in ghosts 25 believed in Bigfoot 10 believed in UFOs and ghosts 8 believed in ghosts and Bigfoot 5 believed in UFOs and Bigfoot 2 believed in all three Draw and label a Venn diagram to determine how many people believed in at least one of these things. Starting with the intersection of all three circles, we work our way out. The number in the center is 2, since two people believe in UFO’s, ghosts and Bigfoot. Since 10 people believe in UFOs and Ghosts, and that includes the 2 that believe in all three, that leaves 8 that believe in only UFOs and Ghosts.
Here is an example of a Venn diagram with three sets. Example 8: In a survey, adults were asked how they travel to work. Below is the recorded data on how many people bused, biked, and/or drove to work. Draw and label a Venn diagram using the information in the table. Travel Options Frequency Just Car 157 Just Bike 20 Just Bus 35 Car and Bike only 35 Car and Bus only 10 Bus and Bike only 8 Car, Bus and Bike 12 Neither Car, Bus nor Bike 15 292 To fill in the Venn diagram, we will place the 157 people who only drive a car in the car set where it does not overlap with any other modes of transportation. We can fill in the numbers 20 and 35 in a similar way. Then we have the overlap of two modes of transportation only. There are 35 people who use their car and bike only, so they go in the overlap of those two sets, but they do not take the bus, so they are outside of the bus set. Similarly, we can enter the 10 and 8. There are 12 people who use all three modes, so they are in the intersection of all three sets. There are 15 people who do not use any of the three modes, so they are placed outside the circles but inside the universal set of all modes of transportation. Here is the completed Venn diagram. Example 9: One hundred fifty people were surveyed and asked if they believed in UFOs, ghosts, and Bigfoot. The following results were recorded. 43 believed in UFOs 44 believed in ghosts 25 believed in Bigfoot 10 believed in UFOs and ghosts 8 believed in ghosts and Bigfoot 5 believed in UFOs and Bigfoot 2 believed in all three Draw and label a Venn diagram to determine how many people believed in at least one of these things. Starting with the intersection of all three circles, we work our way out. The number in the center is 2, since two people believe in UFO’s, ghosts and Bigfoot. Since 10 people believe in UFOs and Ghosts, and that includes the 2 that believe in all three, that leaves 8 that believe in only UFOs and Ghosts.
Chapter1-Logic-and-Sets9-4-18.docx