a word problem on Sets and relations

Topic:-Sets and Relations

A set is a group or collection of objects or numbers, considered as an entity unto itself. Sets are usually symbolized by uppercase, italicized, boldface letters such as A, B, S, or Z.
Each object or number in a set is called a member or element of the set.

Examples include the set of all computers in the world, the set of all apples on a tree, and the set of all irrational numbers between 0 and 1.

Let's see a word problem on this.

Question:-

In an elementary school, students know atleast one of the languages, French and Spanish. 125 students know French, 75 students know Spanish and 50 of them know both French and Spanish. How many students are there in the school?

Answer:-

Let:

n(F) = number of students who know French

n(S) = number of students who know Spanish

Here

n(F) = 125, n(S) = 78, n(F n S) = 50

We have to find n(F u S)

We know that n(F u S) = n(F) + n(S) - n(F n S)
= 125 + 75 - 50
= 150 (Answer)

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