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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How to find slope of two points

Topic:- Slope
Slope is used to describe the steepness, incline, gradient, or grade of a straight line. A higher slope value indicates a steeper incline. The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between two points on the line. It is also always the same thing as how many rises in one run.

To find slope of two points when there is two points given ,we have to use the slope formula .


Question :-

Find the slope of (2,4) (3,7)

Answer:-

This math help is to find the slope

Let us assume that,

( 2 , 4 ) ( 3 , 7 )
x1   y1   x2  y2


The formula for slope is

 y2-y1
----------
 x2-x1

 7- 4
-------
 3- 2

  3
-----
  1

= 3 is the slope

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