Lesson Logic problems - The solution to Problem 4

Source code of 'Logic problems - The solution to Problem 4'

This Lesson (Logic problems - The solution to Problem 4) was created by by ikleyn(52778)

: View Source, Show
About ikleyn:

<H2>The solution to Problem 4</H2>

Below &nbsp;(after the &nbsp;reminder)&nbsp; is the &nbsp;solution&nbsp; to the &nbsp;Problem 4&nbsp; of the lesson &nbsp;<A HREF = http://www.algebra.com/algebra/homework/word/misc/Some-logic-problems.lesson>Some logic problems</A>&nbsp; (the topic &nbsp;Miscellaneous word problems 
of the section &nbsp;Word problems&nbsp; in this site).

<BLOCKQUOTE>Problem 4 formulation (reminder)

There are &nbsp;25&nbsp; students in the class.
Each student attends a sport class or an art school. &nbsp;Some of students attend both the sport class and the art school.
The number of students attending the sport class is &nbsp;18; &nbsp;the number of students attending the art school is &nbsp;12.
How many of class students attend both the sport class and the art school?</BLOCKQUOTE>

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, &nbsp;the number of students who attend both the sport class and the art school, &nbsp;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 &nbsp;5.

<BLOCKQUOTE>Note

Let us consider the problem generalization.
Suppose you have the finite set of &nbsp;{{{N}}}&nbsp; elements, &nbsp;and two its subsets consisting of &nbsp;{{{N[1]}}}&nbsp; and &nbsp;{{{N[2]}}}&nbsp; elements respectively.

If these subsets, &nbsp;taken together, &nbsp;cover the entire set, &nbsp;then the number of elements in the subsets intersection is equal to &nbsp;{{{(N[1]+N[2])-N}}}.

The proof is very similar to the &nbsp;Problem 4&nbsp; solution.</BLOCKQUOTE>

<A HREF = http://www.algebra.com/algebra/homework/word/misc/Some-logic-problems.lesson>Back to the original lesson &nbsp;Some logic problems</A>&nbsp; (the topic &nbsp;Miscellaneous word problems&nbsp; of the section &nbsp;Word problems&nbsp; in this site).