Definition of relation, Mathematics

Assignment Help:

Definition of Relation

A relation is a set of ordered pairs.

It seems like an odd definition however we'll require it for the definition of a function though, before actually we give the definition of a function let's see if we can get a handle on just what a relation is.

In example we constructed a set of ordered pairs we used to sketch the graph of that we used.

                            y =( x -1)2  - 4

2328_Definition of Relation.png

Here are the ordered pairs of this graph

( -2, 5)( -1, 0)(0, -3)(1, -4)(2, -3)(3, 0)( 4, 5)

Thenany of the following are relations since they consist of a set of ordered pairs.

{( -2, 5)  ( -1, 0)  ( 2, -3)}

{( -1, 0)  (0, -3) ( 2, -3)  (3, 0)  ( 4, 5)}

{(3, 0)  ( 4, 5)}

{( -2, 5)  ( -1, 0)  (0, -3) (1, -4)  ( 2, -3)  (3, 0)  ( 4, 5)}

Of course there are several more relations which we could make from the list of ordered pairs above, however we just desired to list a few possible relations to give some instance.  Notice as well that we could get other ordered pairs also from the equation and add those into any of the relations above if we desired to.

Now, at this point you are possibly asking just why we care about relations & that is a good question. Some relations are extremely special and are utilized at almost all levels of mathematics. Given definition tells us just which relations are these special relations.


Related Discussions:- Definition of relation

Solution of rectilinear figures, A tower and a monument stand on a level pl...

A tower and a monument stand on a level plane. the angles of depression on top and bottom of the monument viewed from the top of the tower are 13 degrees and 31 degrees, respective

How to left shifts and right shifts a graph, Q. How to Left shifts and righ...

Q. How to Left shifts and right shifts a graph? Ans. When you're translating (shifting) a graph, it's easy to get subtracting and adding mixed up. It seems counter-intuiti

Percentage change, in a sale a clothes shop reduces its prices by 30% a shi...

in a sale a clothes shop reduces its prices by 30% a shirt usually costs £38 how much is it in the sale

What is the radius of the traffic circle, In traveling three-fourths of the...

In traveling three-fourths of the way around a traffic circle a car travels 0.228 mi.  What is the radius of the traffic circle? The radius of the traffic circle is ____ mi.

An initial species population , An initial species population is y(0) = 300...

An initial species population is y(0) = 3000. At t=0 the population starts to grow exponentially with a doubling time of 2 years. Mark the only correct statement: a)    The per

prove area of rhombus on hypotenuse right-angled triangle, Prove that the ...

Prove that the area of a rhombus on the hypotenuse of a right-angled triangle, with one of the angles as 60o, is equal to the sum of the areas of rhombuses with one of their angles

Algebra, 1 ream uses 6% of a tree, Estimate the reams of paper used in one ...

1 ream uses 6% of a tree, Estimate the reams of paper used in one month in an office(may be your father, mother or neighbour), hence find the number of trees that need to be cut fo

The mean value theorem with proof, The Mean Value Theorem  Assume f(x)...

The Mean Value Theorem  Assume f(x) is a function that satisfies both of the subsequent. 1.   f(x) is continuous on the closed interval [a,b]. 2.   f(x) is differentiabl

Geometry, Given: ??????? is supp. to ??????? ???? ????? bisects ??????? ?...

Given: ??????? is supp. to ??????? ???? ????? bisects ??????? ???? ????? bisects ??????? Prove: ??????? is a rt. ?

Example of rounding off, Example of Rounding Off: Example: Round ...

Example of Rounding Off: Example: Round off the subsequent number to two decimal places. 6.238 Solution: Step 1:             8 is the number to the right of t

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd