**Question:**

During the physical training movement, students in the $ 10A $ class participate in table tennis or volleyball or both. Knowing that there is $ 21 $ for children to play volleyball, $ 37 $ for table tennis and $ 13 $ for both. Ask how many students are there in the $ 10A $ class.

**Answer**

Repeat:

Given two sets $ A, B $, denote $ n (X) $ is the number of elements of the set $ X $. We have:

$ n (A) + n (B) = n (A \cap B) + n (A \cup B) $.

This can be demonstrated by drawing a graph. Venn.

Now call $ A $ the set of students playing volleyball.

$ B $ is the collection of students playing table tennis.

$ A \cap B $ is a collection of performances for students to participate in both subjects.

And $ A \cup B $ is a collection of student numbers for the whole class.

Applying the above formula,

The number of students in class $ 10A $ is: $ n (A \cup B) = n (A) + n (B) – n (A \cap B ) = 21 + 37 – 13 = $ 45 students.

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