Answer:
25
Step-by-step explanation:
We'll compare it with the study of sets, the most noticeable operation of which is:
- <u>n(A ∪ B) = n(A) + n(B) - n(A ∩ B)</u>
where,
n(A ∪ B) is the Union Set, i. e, the set that contains all the elements
n(A) is a subset of the Union Set
n(B) is another subset of the Union Set, and
n(A ∩ B) is the Intersection Set ,i.e, the set contains common elements from both A and B sets.
<h3><u>In the question:</u></h3>
- n(A ∪ B) = ? (<em>the total number of students in the class who are into the above mentioned sports)</em>
Let set A contains the students who play basketball and set B, the students who play Volleyball.
10 students play both of them, i. e.,
- n(A ∩ B) = 10 (<em>as 10 students have common sports - Volleyball and Basketball</em>)
<u>Using the above operation:</u>
=> n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
=> n(A ∪ B) = 25 + 20 - 10
=> n(A ∪ B) = 35
<h3><u>Final Step to the Answer:</u></h3>
<u>The total number of students in the class </u>
= students into the given sports + students who don't play any of them
- Total number of students in the class is 60
- Total number fo students playing basketball and volleyball is 35
The students who play neither = 60 - 35
= 25
