Conjuntos

EJERCICIOS

1º. Si:

A={x€Z/x3 -5x2+4x=0}

B={x€Q/(x-1)(x+2)(2x-3)(2x2+x-6)=0}

Hallar: a). A∩B b). AUB c). A-B d). A∆B

Desarrollo

A={0,1,4} ; B={1,-2,3⁄2}

A∩B={1} c) A-B={0,4}

AUB={0,1,-2,4,3⁄2} d) A∆B={0,-2,4,3⁄2,2,4}

2º.Si:

A={x€Q/(x+1)(x-1⁄2)(x2+7x+10)=0}

B={x€R/(x2-3x-10)(x-3)(x+1)(2x-1)=0}

C={x€Z/-1≤x≤3}

Hallar: a). A-B b). (A∩B)-(AUC) c). (A∩B)-C d). (B-C)∩(A-C)

Desarrollo

A={-1,1⁄2,-2,-5} ; B={5,-2,3,-1,1⁄2} ; C={-1,0,1,2,3}

a)A-B={-5}

b)(A∩B)-(A∪C)={∅}

c)(A∩B)-C={-1,-2,1⁄2}-{-1,0,1,2,3}={-2,1⁄2}

d)(B-C)∩(A-C)={5,-2,1⁄2}∩{1⁄2,-2,-5}={-2,1⁄2}

3º.Si:

U={x€R/-5≤x≤8}

A={x€U/(x+6)(x2-3x-40}=0}

B={x€U/(x2-4x-21)(x3+9x)(x2-12x+35)=0}

Hallar: a). A’ b). B’ c). (A-B)’ d). (A-B)’U(B-A)’

Desarrollo

U={-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8} ; A={-5,8} ; B={-3,0,5,7}

a)A^'={-4,-3,-2,-1,0,1,2,3,4,5,6,7}

b)B^'={-5,-4,-2,-1,1,2,3,4,6,8}

c)(A-B)^'→{-5,8}={-4,-3,-2,-1,0,1,2,3,4,5,6,7}

d)(A-B)^'∪(B-A)^'→{-5,8}∪{-3,0,5,7}=

{-4,-3,-2,-1,0,1,2,3,4,5,6,7}∪{-5,-4,-3,-2,-1,1,2,3,4,6,8}=

{-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8}

4º.Si:

U={x€Z/-2≤x≤7}

A={x€Z/x3-4x=0}

B={x€Z/x3-3x2-6x+8=0}

C={x€Q/(x-1)(2x+3)(x-2)(x-4)=0}

Hallar: a). A’ b). A∆B c). (A-B)∩(B-C)’ d). (A∆B)-(B∆C)

Desarrollo

U={-2,-1,0,1,2,3,4,5,6,7} ; A={2,0} ; B={1,-2,4} ; C={1,-3⁄2,2,4}

a)A^'={-2,-1,1,3,4,5,6,7}

b)A∆B={2,0,1,-2,4}

c)(A-B)∩(B-C)^'={2,0}∩{-2}={∅}

d)(A∆B)-(B∆C)={2,0,1,-2,4}-{-2,-3⁄2,2}={0,1,4}

5º.Si:

U={x€Z/-2≤x≤8}

A={x€U/(x2-9)(x3-4x)(x2+3x-10)=0}

B={x€U/x2-2x-35=0}

C={x€U/3≤x≤8}

Hallar: a). A’ b). B’ c). C’ d).(A∩B)’U(B∩C)’ e). (A-B)’-(B-C)’

Desarrollo

U={-2,-1,0,1,2,3,4,5,6,7,8} ; A={3,2} ; B={7} ; C={3,4,5,6,7,8}

a)A^'={-2,-1,0,1,4,5,6,7,8}

b)B^'={-2,-1,0,1,2,3,4,5,6,8}

c)C^'={-2,-1,0,1,2}

d)(A∩B)^'∪(B∩C)^'={∅}^'∪{7}^'=

{-2,-1,0,1,2,3,4,5,6,7,8}∪{-2,-1,0,1,2,3,4,5,6,8}={-2,-1,0,1,2,3,4,5,6,7,8}

e)(A-B)^'-(B-C)^'={2,3}^'-{∅}^'=

{-2,-1,0,1,4,5,6,7,8}-{-2,-1,0,1,2,3,4,5,6,7,8}={∅}

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