There are 60 students studying Sciences (Biology, Chemistry or Physics). 15 students study Biology and Physics. 13 students study Biology and Chemistry. 8 students study Chemistry and Physics. 5 students study all three Sciences. Complete the Venn diagram.

Answer

To solve this problem, we need to fill out a Venn diagram based on the information provided about the students studying different sciences. We will denote: - B for Biology, - C for Chemistry, - P for Physics. 1. Start with the number of students studying all three subjects: - Let’s denote this as x. We know from the question that x = 5, as 5 students study all three sciences. 2. Use the number of students studying pairs of subjects to find out how many study just those pairs: - For Biology and Physics (B∩P): 15 students total. Since 5 of those also study Chemistry, the number of students who study only Biology and Physics, without Chemistry, is: - 15 - 5 = 10. - For Biology and Chemistry (B∩C): 13 students total. Similar to before, since 5 students study all three subjects, the number studying only Biology and Chemistry is: - 13 - 5 = 8. - For Chemistry and Physics (C∩P): 8 students total. Again, subtracting those who study all three gives: - 8 - 5 = 3. 3. Next, let’s find out how many study only one subject: - Let’s denote: - B only = the students studying only Biology, - C only = the students studying only Chemistry, - P only = the students studying only Physics. - We can set the following equations based on the total number of students: - Total = (B only) + (C only) + (P only) + (10 from B∩P) + (8 from B∩C) + (3 from C∩P) + (5 from B∩C∩P) = 60. - Now, simplifying: - B only + C only + P only + 10 + 8 + 3 + 5 = 60, - B only + C only + P only + 26 = 60, - B only + C only + P only = 60 - 26 = 34. 4. Since there are no more constraints to limit B only, C only, and P only, we need more detailed information about individual subject preferences to distribute these 34 students, since the problem does not provide specific counts for those who study only one subject. In summary, we have: - Students studying only Biology = B only - Students studying only Chemistry = C only - Students studying only Physics = P only - Students studying Biology and Physics = 10 - Students studying Biology and Chemistry = 8 - Students studying Chemistry and Physics = 3 - Students studying all three subjects = 5 From our setup, we can summarize these findings into the Venn diagram, with the counts found for each intersection. Overall, specifics for each solitary science cannot be determined without more data.