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 Group members NG Duyên Thu Trang Hoa Mai I COMPENSATION Formula 1: PRINCIPLE Given sets A, B We have: FORMULA 2: Given X set and n is a subset In which: We have: 3.THE PRINCIPLE OF COMPENSATION (SIEVE'S FORMULA) IS: II PRINCIPLE OF GENERALIZED COMPENSATION DEFINITION THEOREM 1.DEFINITION Consider m objects These objects are respectively attached to weights which are the elements of some commutative ring K Each given object may or may not have properties where Symbol 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, IV APPLICATIONS THE PRINCICPLE OF COMPENSATION TO SOLVE THE PROBLEM OF EXTENDING THE COMMON VENN DIAGRAM BY THE PRINCIPLE OF OFFSET EXERCISES NUMBER COUNTING PROBLEM SATISFYING ARITHMETIC PROPERTIES THE PROBLEM OF COUNTING THE NUMBER OF INTEGER SOLUTIONS BERNOULLI – EULER PROBLEM SURJECTIVE COUNT MATH PROBLEM THE PRINCIPLE OF COMPENSATION COMBINES WITH THE MAPPING METHOD Thank You For Listening  ... is N, then we deduce that: N( …) = N On the other hand, by the principle of compensation we have : = - + –…+ Hence, IV APPLICATIONS THE PRINCICPLE OF COMPENSATION TO SOLVE THE PROBLEM OF EXTENDING... where Symbol 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... I COMPENSATION Formula 1: PRINCIPLE Given sets A, B We have: FORMULA 2: Given X set and n is a subset In which: We have: 3 .THE PRINCIPLE OF COMPENSATION (SIEVE'S FORMULA) IS: II PRINCIPLE OF