Question

out of 60 students, 25 are taking english, 32 are taking math, and 15 are in both classes. use venn diagram below to organize the information. complete the venn diagram by entering the number of elements in each region and answer the questions below: region i = region ii = region iii = region iv = how many students are in english or math? how many students are not in english? how many students are in english and not in math?

Explanation:

Step1: Find number in Region I

Region I is students in English only. So we subtract number in both from number in English. $25 - 15=10$.

Step2: Find number in Region II

Region II is students in both English and Math, which is given as 15.

Step3: Find number in Region III

Region III is students in Math only. Subtract number in both from number in Math. $32 - 15 = 17$.

Step4: Find number in Region IV

Region IV is students in neither English nor Math. First find number in English or Math using formula $n(E\cup M)=n(E)+n(M)-n(E\cap M)=25 + 32-15=42$. Then subtract from total students. $60 - 42=18$.

Step5: Find number of students in English or Math

Using the formula $n(E\cup M)=n(E)+n(M)-n(E\cap M)=25 + 32 - 15=42$.

Step6: Find number of students not in English

Total students minus students in English. $60 - 25=35$.

Step7: Find number of students in English and not in Math

This is number of students in Region I, which is 10.

Answer:

Region I = 10
Region II = 15
Region III = 17
Region IV = 18
How many students are in English or Math? 42
How many students are not in English? 35
How many students are in English and not in Math? 10