Actividad 1 - Conceptos básicos de matemática discreta
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Course
Matemáticas Discretas (PIS000028)
Institution
Universidad Manuela Beltrán
Resolver los ejercicios que se presentan en la guía con el fin de trabajar los conceptos básicos de la matemática discreta. Para cada ejercicio se debe argumentar paso a paso cada proceso que lleve a la solución del ejercicio.
TALLER 1: CONCEPTOS BÁSICOS DE LA MATEMÁTICA DISCRETA
José Yovanny Espejo Castellanos
Universidad Manuela Beltrán
Facultad de ingeniería
ingeniería de Software
Bogotá D.C
2021
, 2
Contenido
Descripción de la actividad ……………………………………………………………...3
Conceptos básicos de la matemática discreta ………………………………………..5
Propiedades aritméticas …………………………………………………………5
1. Propiedad clausurativa ……………………………………………….5
2. Propiedad conmutativa ……………………………………………….6
3. Propiedad asociativa ………………………………………………….7
4. Elemento neutro ……………………………………………………….8
5. Distributiva con respecto a la multiplicación ……………………….9
6. Inverso aditivo …………………………………………………………9
7. Transitividad ………………………………………………………….10
Propiedades de orden …………………………………………………………..11
1. Reflexiva ……………………………………………………………...11
2. Antisimétrica…………………………………………………………..11
3. Transitiva………………………………………………………………11
4. …………………………………………………………………………12
5. ………………………………………………………………………….12
Principio de inducción matemática……………………………………………………..13
Teorema fundamental de la aritmética………………………………………………....14
Máximo Común Divisor (M.C.D) ………………………………………………………..15
Funciones aritméticas……………………………………………………………………17
Ecuaciones Diofánticas lineales ………………………………………………………..21
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Descripción de la actividad
,4
, 5
SOLUCION
PROPIEDADES ARITMETICAS 1
R/ 19, 11 y 22 son números enteros. R/ 10, 19 y 13 son números enteros.
R/ 60, 28 y 105 son números enteros. R/ 16, 88 y 22 son números enteros.
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PROPIEDADES ARITMETICAS 2
a+b = b+a
a*b = b*a
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