The principle of compensation and its application

The principle of compensation and its application THE PRINCIPLE OF COMPENSATION AND ITS APPLICATION NG Duyên Group members Hoa Mai Thu Trang Given 2 sets A, B We have 1 Formula 1 I COMPENSATION PRINCIPLE 2 FORMULA 2 Given X set and n is a subset We have In which 3 THE PRINCIPLE OF COMPENSATION (SIEVES FORMULA) IS II PRINCIPLE OF GENERALIZED COMPENSATION DEFINITION THEOREM Consider m objects These objects are respectively attached to weights which are the elements of some commutative ring K Each.

THE PRINCIPLE

OF COMPENSATION

AND ITS APPLICATION

NG Duyên

Group members

Hoa Mai Thu Trang

Given 2 sets A, B We have:

1 Formula 1:

I COMPENSATION

PRINCIPLE

2 FORMULA 2:

Given X set and n is a subset We have:

In which:

3.THE PRINCIPLE OF COMPENSATION (SIEVE'S

FORMULA) IS:

II PRINCIPLE OF GENERALIZED COMPENSATION

DEFINITION

THEOREM

Consider m objects These objects are

elements of some commutative ring K Each given object may or may not have properties Symbol =,

1.DEFINITION

where is the sum of the weights of all objects with properties

M(r) is the sum of the weights of all objects with exactly r properties

is the sum of the weights of all objects with no less than r properties

2 THEOREM

M(r)= ,

for all r = 0.1, ,n

III-GENERAL COMPENSATION

FORMULA

Suppose is a subset containing elements of

property , the number of elements with all

properties , , …is denoted by N(, …) Writing the

above quantities over the sets we have: = N( , …)

If the number of elements that have no

properties among n properties , , …, is denoted by N(…) and the number of elements in the given set

is N, then we deduce that: N( …) = N

-On the other hand, by the principle of

compensation we have :

= - + –…+

Hence,

N( …) = N - + - +…+ …)

IV APPLICATIONS THE PRINCICPLE

OF COMPENSATION TO SOLVE

EXERCISES.

THE PROBLEM OF EXTENDING THE COMMON VENN DIAGRAM BY THE PRINCIPLE OF OFFSET

SURJECTIVE COUNT MATH PROBLEM

BERNOULLI – EULER PROBLEM

THE PROBLEM OF COUNTING THE NUMBER OF INTEGER SOLUTIONS

NUMBER COUNTING PROBLEM SATISFYING ARITHMETIC PROPERTIES

6 THE PRINCIPLE OF COMPENSATION COMBINES WITH THE MAPPING METHOD

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