A word problem on sets

A set is a collection of distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics. Although it was invented at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. In mathematics education, elementary topics such as Venn diagrams are taught at a young age, while more advanced concepts are taught as part of a university degree.

Here is an example from algebra 1 word problems


Question:-

In a school there are 20 teachers who teach mathematics or physics,of these ,12 teach mathematics and 4 teach both physics and mathematics .How many teach physics

Answer:-

The total number of students =20 (this is we call what is Universal Set U)

Let M be the teachers who teach mathematics

and P be the teachers who teach physics.

the word 'or' gives a clue of union and the word 'and' gives a clue of intersection.

n(M U P)=20

n(M)=12

n(M Ω P)=4

you can see a example of Venn diagram

using the formula

n(M U P)=n(M)+n(P)-n(M Ω P)

20 = 12+n(P)-4

20 = 8+n(P)

subtract 8 on both sides

12 = n(P)

So 12 teachers teach physics