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 of students only in English

The number of students taking English is 25 and 15 are in both English and Math. So the number of students only in English (Region I) is $25 - 15=10$.

Step2: Identify number of students in both

The number of students in both English and Math (Region II) is given as 15.

Step3: Find number of students only in Math

The number of students taking Math is 32 and 15 are in both English and Math. So the number of students only in Math (Region III) is $32 - 15 = 17$.

Step4: Find number of students in neither

The total number of students is 60. The number of students in English or Math is $10+15 + 17=42$. So the number of students in neither (Region IV) is $60-42 = 18$.

Step5: Find number of students in English or Math

Using the principle of inclusion - exclusion, the number of students in English or Math is $n(E\cup M)=n(E)+n(M)-n(E\cap M)=25 + 32-15=42$.

Step6: Find number of students not in English

The number of students not in English is the sum of students only in Math and students in neither, which is $17+18 = 35$.

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

The number of students in English and not in Math is the number of students only in English, 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