Conjuntos lógica

1. Sean los conjuntos:

U = {a,b,c,d,e,f,g,h,i,j}

A = {f,g,i,j}

B = {a,c,d,f,h,i}

C = {c,d,e,f,g,h}

D = {a,b,c}

Encontrar:

a) (AB) (CD)         ={a,c,d,f,g,h}[pic 1][pic 2][pic 3]

b) ((AD) B)  C         ={e,g}[pic 4][pic 5][pic 6]

c) (ACD)'B                 ={a,b,c,d,e,f,g,h,i,j}         ={U}[pic 7][pic 8][pic 9]

d) (D B) A'                ={a,b,c,d,e,f,h}[pic 10][pic 11]

e) ((A B)  (D  B))  (CD')                =[pic 12][pic 13][pic 14][pic 15][pic 16][pic 17]

1. Sean los conjuntos:

U = {x l xR} [pic 18]

A = {x l xR; 1 = 0} [pic 19][pic 20]

B = {-1,2, 4)

Encontrar:

a) (A  B)'                ={x l xR; excepto -1,1,2,4}[pic 21][pic 22]

 b) (A B)'                 ={x l xR; excepto -1}[pic 23][pic 24]

c) (B  A')                 ={-1}[pic 25]

d) (AB) B'         ={x l xR; excepto -1,1,2,4}[pic 26][pic 27][pic 28]

e) (B  (BA)') A        ={1}[pic 29][pic 30][pic 31]

III.        Sean los conjuntos:

          U = {x l x  ; 0 < x < 100 }[pic 32][pic 33]

        A = {x l x x es par; x < 10 }[pic 34]

        B = {1,2,4,5,6,7}

        C = {x l x  ; x es divisible entre 3; x < 16[pic 35][pic 36]

        Encontrar:

        a) (AB)'C                 ={x l x  ; 0 < x < 100; excepto 2,3,4,6,8,9,12,15}[pic 37][pic 38][pic 39][pic 40]

        b) (AC) B'                ={3,8,9,12,15}[pic 41][pic 42]

        c) (C B)'A'                 ={x l x  ; 0 < x < 100; excepto 2,3,4,6,8,9,12,15}[pic 43][pic 44][pic 45][pic 46]

        d) (BA) (C'A)        ={8}[pic 47][pic 48][pic 49]

         e) ((CB) C') A        ={x l x  ; 0 < x < 100; excepto 2,3,4,6,8,9,12,15}[pic 50][pic 51][pic 52][pic 53][pic 54]

IV.        Sean los conjuntos:

        U = {x l x  ; 0 < x <5000} [pic 55][pic 56]

        A = {x l x  ; x es par; 0 < x <30} [pic 57]

        B = {7, 8, 9 , 13, 21,28}

        C = {x l x  ; es primo; 0 < x < 20} [pic 58][pic 59]

        D = {4, 6, 8, 10, 12, 14, 16}

        Encontrar:

        a) ((A  B)  (C  B))'         ={x l x ∈ ; 0 < x <5000; excepto 9,21, x l x ∈ ; x es par; 0 < x <30; excepto 8,28}[pic 60][pic 61][pic 62][pic 63][pic 64]

        b) ((A' C') B')  D'         ={x l x ∈ ; 0 < x <5000; excepto 3,4,5,6,8,10,11,12,14,16,17,19,21,28}[pic 65][pic 66][pic 67][pic 68]

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