Atps Matematica Aplicada 4 Anhanguera

Etapa 1
2.1 Passo 1 06
2.2 Passo 2 08
2.3 Passo 3 10

Etapa 2
2.4 Passo 1 12
2.5 Passo 2 14
2.6 Passo 3 14

Etapa 1





2.1 Passo 1
L1={6,8} l1’={1,2,3,4,5,7,9}
C1={2} c1’={1,3,4,5,6,7,8,9}
S1={6,9} s1’={1,2,3,4,5,7,8}

L2={9} l2’={1,2,3,4,5,6,7,8}
C2={1,8} C2’={2,3,4,5,6,7,9}
S2={2,4} S2’={1,3,5,6,7,8,9}

L3={2,4,6} L3’={1,3,5,7,8,9}
C3={5,6,9} C3’={1,2,3,4,7,8}
S3={6,8} S3’={1,2,3,4,5,7,9}

L4={1,8} L4’={2,3,4,5,6,7,9}
C4={1,8} C4’={2,3,4,5,6,7,9}
S4={1,8} S4’={2,3,4,5,6,7,9}

L5={1,2} L5’={3,4,5,6,7,8,9}
C5={3,4} C5’={1,2,5,6,7,8,9}
S5={1,9} S5’={2,3,4,5,6,7,8}

L6={4,9} L6’={1,2,3,5,6,7,8}
C6={2,9} C6’={1,3,4,5,6,7,8}
S6={2,4} S6’={1,3,5,6,7,8,9}

L7={1,3,8} L7’={2,4,5,6,7,9}
C7={1,8,9} C7’={2,3,4,5,6,7}
S7={2,5} S7’={1,3,4,6,7,8,9}

L8={9} L8’={1,2,3,4,5,6,7,8}
C8={2,4} C8’={1,3,5,6,7,8,9}
S8={3,8} S8’={1,2,4,5,6,7,9}

L9={2,5} L9’={1,3,4,6,7,8,9}
C9={6} C9’={1,2,3,4,5,7,8,9}
S9={1,9} S9’={2,3,4,5,6,7,8}













2.2 Passo 2
|Linha 1 sub-grade 1 |Linha 1 sub-grade 2 |Linha 1 sub-grade 3 |
|SDK1,1={1,3,4,5,7} |SDK1,4={3,5,7,9} |SDK1,7={2,3,4,5,7} |
|SDK1,2={2,3,4,5,7} |SDK1,5={1,5,7,9} |SDK1,8={1,3,5,7,9} |
|SDK1,3={1,2,3,4,7} |SDK1,6={1,3,5,7} |SDK1,9={1,2,3,4,5,7,9} |
|Linha 2 sub-grade 1 |Linha 1 sub-grade 2 |Linha 2 sub-grade 3

|SDK2,1={1,3,4,5,7,8} |SDK2,4={3,5,6,7} |SDK2,7={2,3,4,5,7} |
|SDK2,2={2,3,4,5,7} |SDK2,5={1,5,6,7,8} |SDK2,8={1,3,5,7} |
|SDK2,3={1,2,3,4,7,8} |SDK2,6={1,3,5,6,7,8} |SDK2,9={1,2,3,4,5,7} |
|Linha 3 sub-grade 1 |Linha 3 sub-grade 2 |Linha 3 sub-grade 3 |
|SDK3,1={1,3,5,7,8} |SDK3,4={3,5,7,9} |SDK3,7={3,5,7} |
|SDK3,2={3,5,7} |SDK3,5={1,5,7,8,9} |SDK3,8={1,3,5,7,9} |
|SDK3,3={1,3,7,8} |SDK3,6={1,3,5,7,8} |SDK3,9={1,3,5,7,9} |
|Linha 4 sub-grade 4 |Linha 4 sub-grade 5 |Linha 4 sub-grade 6 |
|SDK4,1={3,4,5,6,7,9} |SDK4,4={2,3,4,5,6,7} |SDK4,7={3,5,6,7} |
|SDK4,2={2,3,4,5,6,7,9} |SDK4,5={2,5,6,7} |SDK4,8={3,5,6,7,9} |
|SDK4,3={2,3,4,7} |SDK4,6={3,4,5,6,7} |SDK4,9={3,5,7,9} |
|Linha 5 sub-grade 4 |Linha 5 sub-grade 5

Linha 5 sub-grade 6 |
|SDK5,1={3,4,5,6,7,9} |SDK5,4={3,4,5,6,7} |SDK5,7={3,5,6,7} |
|SDK5,2={3,4,5,6,7,9} |SDK5,5={5,6,7,8} |SDK5,8={3,5,6,7,8,9} |
|SDK5,3={3,4,7} |SDK5,6={3,4,5,6,7,8} |SDK5,9={3,5,7,8,9} |
|Linha 6 sub-grade 4 |Linha 6 sub-grade 5 |Linha 6 sub-grade 6 |
|SDK6,1={3,5,6,7} |SDK6,4={2,3,5,6,7} |SDK6,7={3,5,6,7} |
|SDK6,2={2,3,5,6,7} |SDK6,5={2,5,6,7,8} |SDK6,8={1,3,5,6,7,8} |
|SDK6,3={2,3,7} |SDK6,6={3,5,6,7,8} |SDK6,9={1,3,5,7,8} |
|Linha 7 sub-grade 7 |Linha 7 sub-grade 8 |Linha 7 sub-grade 9 |
|SDK7,1={4,6,7,9} |SDK7,4={2,4,5,6,7,9} |SDK7,7={2,4,5,6,7} |
|SDK7,2={4,6,7,9} |SDK7,5={2,5,6,7,9} |SDK7,8={5,6,7} |
|SDK7,3={4,7} |SDK7,6={4,5,6,7} |SDK7,9={2,4,5,7} |

Linha 8 sub-grade 7 |Linha 8 sub-grade 8 |Linha 8 sub-grade 9 |
|SDK8,1={1,3,4,6,7,8} |SDK8,4={2,4,5,6,7} |SDK8,7={2,3,4,5,6,7} |
|SDK8,2={3,4,6,7} |SDK8,5={1,2,5,6,7} |SDK8,8={3,5,6,7,8} |
|SDK8,3={1,3,4,7,8} |SDK8,6={1,4,5,6,7} |SDK8,9={2,3,4,5,7,8} |
|Linha 9 sub-grade 7 |Linha 9 sub-grade 8 |Linha 9 sub-grade 9 |
|SDK9,1={1,3,4,6,7,8,9} |SDK9,4={4,6,7,9} |SDK9,7={3,4,6,7} |
|SDK9,2={3,4,6,7,9} |SDK9,5={1,6,7,9} |SDK9,8={3,6,7,8} |
|SDK9,3={1,3,4,7,8} |SDK9,6={1,4,6,7} |SDK9,9={3,4,7,8} |










2.3 Passo 3
No passo 1 foi aplicada a teoria de conjuntos para determinar os conjuntos e para encontrar o complemento de cada conjunto.
L1 e seu complemento L1’ C1 e seu complemento C1’ S1 e seu complemento S1’
L2 e seu complemento L2’ C2 e seu complemento C2’ S2 e seu complemento S2’
L3 e seu complemento L3’ C3 e seu complemento C3’ S3 e seu complemento S3’
L4 e seu complemento L4’ C4 e seu complemento C4’ S4 e seu complemento S4’
L5 e seu complemento L5’ C5 e seu complemento C5’ S5 e seu complemento S5’
L6 e seu complemento L6’ C6 e seu complemento C6’ S6 e seu complemento S6’
L7 e seu complemento L7’ C7 e seu complemento C7’ S7 e seu complemento S7’
L8 e seu complemento L8’ C8 e seu complemento C8’ S8 e seu complemento S8’
L9 e seu complemento L9’ C9 e seu complemento C9’ S9 e seu complemento S9’
No passo2 foi aplicado teoria dos conjuntos usando interseção entre os conjuntos complementares encontrados no passo 1, para achar as possibilidades de cada casa.
|SDK1,1=L1’∩C1’∩S1’ |SDK1,4=L1’∩C4’∩S2’ |SDK1,7=L1’∩C7’∩S3’ |
|SDK1,2=L1’∩C2’∩S1’ |SDK1,5=L1’∩C5’∩S2’ |SDK1,8=L1’∩C8’∩S3’ |
|SDK1,3=L1’∩C3’∩S1’ |SDK1,6=L1’∩C6’∩S2’ |SDK1,9=L1’∩C9’∩S3’ |
|SDK2,1=L2’∩C1’∩S1’ |SDK2,4=L2’∩C4’∩S2’ |SDK2,7=L2’∩C7’∩S3’ |
|SDK2,2=L2’∩C2’∩S1’ |SDK2,5=L2’∩C5’∩S2’ |SDK2,8=L2’∩C8’∩S3’ |
|SDK2,3=L2’∩C3’∩S1’ |SDK2,6=L2’∩C6’∩S2’ |SDK2,9=L2’∩C9’∩S3’ |
|SDK3,1=L3’∩C1’∩S1’ |SDK3,4=L3’∩C4’∩S2’ |SDK3,7=L3’∩C7’∩S3’ |
|SDK3,2=L3’∩C2’∩S1’ |SDK3,5=L3’∩C5’∩S2’ |SDK3,8=L3’∩C8’∩S3’ |
|SDK3,3=L3’∩C3’∩S1’ |SDK3,6=L3’∩C6’∩S2’ |SDK3,9=L3’∩C9’∩S3’ |
|SDK4,1=L4’∩C1’∩S4