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Taller relaciones binarias

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Taller relaciones binarias

  1. 1. Taller relaciones binarias Cristian Andrés Sierra Ospina
  2. 2. 1. A={3,4,5,7} B={4,6,8,10}R={(a,b) tal que a+b<12}R= {(3,4)(3,6)(3,8)(4,4)(4,6)(5,4)(5,6)(7,4)}DomR={3,4,5,7}RanR={4,6,8} SIMPLE
  3. 3. 2. A={1,2,3}R={(1,1)(1,2)(1,3)(2,1)(2,2)(2,3)(3,1)(3,2)(3,3)}DomR={1,2,3}RanR={1,2,3} EQUIVALENTE
  4. 4. 3. A={a,e,i,b,c,d} R= “el primer componente es vocal y el segundo una consonante” R={(a,b)(a,c)(a,d)(e,b)(e,c)(e,d)(i,b)(i,c)(i,d)} DomR={a,e,i} RanR={b,c,d}dcbiea a e i b c d
  5. 5. 4. A={1,2,3,4}R= “(x,y) tal que x es mayor o igual que 2”R={(2,1)(2,2)(2,3)(2,4)(3,1)(3,2)(3,3)(3,4)(4,1)(4,2)(4,3)(4,4)DomR={2,3,4}RanR={1,2,3,4} TRANSITIVA
  6. 6. 5. A={1,2,3,4,5}a. Z=“(x,y) tal que x+y=7”Z={(2,5)(3,4)(4,3)(5,2)}DomZ={2,3,4,5}RanZ={2,3,4,5} SIMÉTRICA
  7. 7. b. Y=“(x,y) tal que x+y sea igual o menor a 4”Y={(1,1)(1,2)(1,3)(2,1)(2,2)(3,1)}DomY={ 1,2,3}RanY={1,2,3} TRANSITIVA Y SIMÉTRICA
  8. 8. 6. A={1,2,3,4}R₁={(1,1)(1,2)(4,3)(2,2)(3,1)(3,2)(4,1)(4,2)}DomR₁={1,2,3,4}RanR₁={1,2,3} TRANSITIVA
  9. 9. R₂={(1,1)(2,1)(2,2)(3,3)(1,2)(1,3)}DomR₂={1,2,3}RanR₂={1,2,3} TRANSITIVA
  10. 10. 7. A={1,2,3…..9}R₁=“(x,y) tal que y=x²”R₁={(1,1)(2,4)(3,9)(0,0)}DomR₁={0,1,2,3}RanR₁={0,1,4,9} TRANSITIVA
  11. 11. R₂=“(x,y) tal que y=2x+1R₂={(1,3)(2,5)(3,7)(4,9)(0,1)DomR₂={0,1,2,3,4}RanR₂={1,3,5,7,9} SIMPLE
  12. 12. R₃=“(x,y) tal que x<4 y y>7”R₃={(0,8)(0,9)(1,8)(1,9)(2,8)(2,9)(3,8)(3,9)}DomR₃={0,1,2,3}RanR₃={8,9} TRANSITIVA
  13. 13. 8. A={-2,-1,0,1,2}R=“(x,y) tal que x²+y²=5”R={(-2,-1)(-2,1)(-1,-2)(-1,2)(1,-2)(1,2)(2,-1)(2,1)}DomR={-2,-1,1,2}RanR={-2,-1,1,2} SIMÉTRICA
  14. 14. 9. A={-5,-4,-3,-2,-1,0,1,2,3,4,5}R=“(x,y) tal que 2x<y”R={(-5,-5)(-5,-4)(-5,-3)(-5,-2)(-5,-1)(-5,0)(-5,1)(-5,2)(-5,3)(-5,4)(-5,5)(-4,-5)(-4,-3)(-4,-2)(-4,-1)(-4,0)(-4,1)(-4,2)(-4,3)(-4,4)(-4,5)(-3,-5)(-3,-4)(-3,-3)(-3,-2)(-3,-1)(-3,0)(-3,1)(-3,2)(-3,3)(-3,4)(-3,5)(-2,-3)(-2,-2)(-2,-1)(-2,0)(-2,1)(-2,2)(-2,3)(-2,4)(-2,5)(-1,-1)(-1,0)(-1,1)(-1,2) (-1,3)(-1,4)(-1,5)(0,1)(0,2)(0,3)(0,4)(0,5)(1,3)(1,4)(1,5)(2,5)}DomR={-2,-1,0,1,2,}RanR={-3,-2,-1,0,1,2,3,4,5} TRANSITIVA
  15. 15. 10. T={-3,-2,-1,0,1,2,3}Z=“(x,y) tal que y-x-1=0Z={(-3,-2)(-2,-1)(-1,0)(0,1)(1,2)(2,3)}DomZ={-3,-2,-1,0,1,2}RanZ={-2,-1,0,1,2,3}SIMPLE

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