SOLUTION: Solved the following using Venn diagram A group of 35 students performed in a school program. out of the 35,18 sang,19,danced, and 7 sang and danced a. How many students sang

Having problem like this, first step is to check if the data is consistent.


So, we check how many people are engaged/involved in the described activiries.


For it, we calculate the number of those, who are involved in any of singing or dancing.


Their number is  18 + 19 - 7 = 30.


It means that of the group of 35 people, 5 perform some other activities other than singing or dancing.


Now I can answer the problem's questions.



(a)  To find how many sang only, subtract from singing those who involved in both singing and dancing

             18 - 7 = 11 people sang only.    ANSWER



(b)  To find how many danced only, subtract from dancing those who involved in both singing and dancing

             19 - 7 = 12 people danced only.    ANSWER



(c)  The number of those who neither sang or danced is  35 - 30 = 5.    ANSWER