Practica Dirigida N

PRACTICA

1.- Sea.

DIRIGIDA N.-1

A = { x є Ν / 3 ≤ x ≤10 } C = { 7, 8, 9, 10 } .

,

B={xєN/x>7}

Hallar : ( A – B ) U

C U (B

-Ac )

SOLUCION A = { x є N / 3 ≤ x ≤ 10 }

B={xєN/x>7}

A = { 3, 4, 5, 6, 7, 8, 9, 10 }

B = { 8, 9, 10, 11, ... }

C = { 7, 8, 9 , 10} Hallar :

(A–B) U

C U ( B ∩Ac )

{ 3, 4, 5, 6, 7 }

U { 7, 8, 9, 10 } U { ( B ∩ Ac ) }

{ 3, 4, 5, 6. 7, 8, 9, 10 }

U∅

{3 ,4, 5, 6, 7, 8, 9, 10 } Rpta.

2.-

11) Dados los conjuntos :

A = { x ∈ R / 1-x22 ∈ < -2 ;4 ] }

B = { x ∈ R / 2x2+ 3x+1 <0 } , } Hallar : ( A- B )

U

(B∩C)

SOLUCION : A = { x ∈ R / 1-x22 ∈ <-2 ;4 ] } -2 < 1-x22 ≤4 -4 <1-x2 ≤ 8 -5 < -x2 ≤ 7 por (-1) -7 ≤ x2 <5 x2 ≥ -7 ⋀ x2 = 7 ⋁ x2> -7

x2 <5 ⋀

x ∈ ∅ ⋁ x ∈R A.

x ∈ <-5 ; 5 >

B = { x ∈R / 2x2+3x+1 <0 }

-5 <x < 5

C = { x ∈ R / x2 >2 → x2 < -2

2x2+3x+1 <0 2x+1x+1<0 Por puntos críticos: x= -12 ; x= -1 x ∈ < -1 ; -12 > C = { x ∈R / x2 >2 → x2 < -2 } x>2

⋁

-2<x<2

⋁

x∈∅ x∈∅

x ∈ <- 2 ; 2 > Hallar : ( A – B ) U ( B ∩ C ) < -5 ; -1 ] U [-12;5 > U < -1 ; -12 > x ∈ < -5 ; 5> Rpta. 3.-

12)

Dado los conjuntos : A = { x ∈R x2-3 ∈[ -3 ;6 > -3 ≤ x2- 3<6 0 ≤ x2 <9

x2≥0 x ∈ < -3 ;3 >

⋀ A=

x ∈ <-3 ;3 >

B = { x ∈R / 3-2x ∈[ -4 ;2 ] -4 ≤3-2x ≤ -1 -7 ≤ -2x ≤ -1 1 ≤2x ≤7

por menos 1

entre 2

12 ≤x ≤72 B = x ∈[ 12 ;72 ]

C = { x ∈ R / x ∈A →x ∈B } x ∈ Ac ⋁ x ∈ B < -∞ ;-3 ] U [ 3 ; +∞ > ⋁ [ 12;72 ] C = { x ∈ < -∞ ; -3 ] U [12 ; + ∞>

D = {x ∈R / x ∈ A ↔ x ∈C } x∈( A ⋀ C ) ⋁

x ∈ ( Ac ⋀ Cc )

x ∈R

[ 12;3 > U ( ( < -∞ ;-3 ] U [ 3 : +∞ >) ⋂ [12 ;3 > U ∅ x ∈R / x∈[ 12;3> Rpta.

<-3 ;12 ] )