Lesson Logic problems - The solution to Problem 4

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The solution to Problem 4

Below (after the reminder) is the solution to the Problem 4 of the lesson Some logic problems (the topic Miscellaneous word problems
of the section Word problems in this site).

Problem 4 formulation (reminder)
There are 25 students in the class.
Each student attends a sport class or an art school. Some of students attend both the sport class and the art school.
The number of students attending the sport class is 18; the number of students attending the art school is 12.
How many of class students attend both the sport class and the art school?

Solution
Add the number of all students attending the sport class and the number of all students attending the art school.
You will get the total number of students in the class plus the number of those students who attend both the sport class and the art school
because you counted twice in this sum those students who attend both the sport class and the art school.

In accordance with this counting, the number of students who attend both the sport class and the art school, is equal to
(18 + 12) - 25 = 30 - 25 = 5.

Answer
The number of students attending both the sport class and the art school is equal to 5.

Note
Let us consider the problem generalization.
Suppose you have the finite set of elements, and two its subsets consisting of and elements respectively.
If these subsets, taken together, cover the entire set, then the number of elements in the subsets intersection is equal to .
The proof is very similar to the Problem 4 solution.

Back to the original lesson Some logic problems (the topic Miscellaneous word problems of the section Word problems in this site).

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