The science club adviser asks some student members what science courses they like. Twenty-eight members say they like physics, 35 say they like chemistry, and a 34 say they like biology. Also, 10 members say they like physics and chemistry, 12 say they like biology and chemistry, 9 say they like physics and biology, and 4 say they like all three. On the other hand, 10 say they do not like any of the three science courses.
Answer (1)
Answer:A Venn diagram is a picture made of circles that shows the relationship between groups (called sets). The overlapping parts of the circles show what the groups have in common, while the parts that don’t overlap show their differences. Its purpose is to help us clearly see how groups are related and how many belong to one group, two groups, or all.So, how do you make a Venn Diagram with the given above?We have three groups of students who like different science courses: Physics (P), Chemistry (C), and Biology (B). Some students also said they don’t like any of the three.Given data:Physics (P) = 28Chemistry (C) = 35Biology (B) = 34Physics & Chemistry = 10Chemistry & Biology = 12Physics & Biology = 9Physics & Chemistry & Biology = 4None = 101. Start with the center (all three):4 students like Physics, Chemistry, and Biology.2. Fill in the overlaps of two groups (subtract the 4 already in the middle):Physics & Chemistry only = 10 − 4 = 6Chemistry & Biology only = 12 − 4 = 8Physics & Biology only = 9 − 4 = 53. Fill in the single groups (subtract those already counted in overlaps):Physics only = 28 − (6 + 5 + 4) = 13Chemistry only = 35 − (6 + 8 + 4) = 17Biology only = 34 − (8 + 5 + 4) = 174. Add those who like none:None = 10Now, we have the final numbers to put in the Venn DiagramPhysics only = 13Chemistry only = 17Biology only = 17Physics & Chemistry only = 6Chemistry & Biology only = 8Physics & Biology only = 5All three = 4None = 10/below is a picture of the Venn Diagram/
