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Let sets A through F be defined as follows.

A = {000}
B = {111}
C = {0x: x ∈ {0, 1}^2}
D = {01x: x ∈ {0, 1}}
E = {1x: x ∈ {0, 1}^2}
F = {00x: x ∈ {0, 1}}

(a) Give two different partitions of the set {0, 1}^3 using one or more of the sets defined above. Give your answer by writing the letters corresponding to the sets in each partition. Ex: A, B, C.

Respuesta :

dammymakins

Answer:

Step-by-step explanation: see attachment below

Ver imagen dammymakins
Ver imagen dammymakins
mirianmoses

Answer:

Step-by-step explanation:

Given that:

Let set A through f be defined as follows

A ={0 0 0}

B ={1 1 1}

C ={Ox: XE {(1,2)²}

D ={ 01x: XE(0,1)}

E = {1X:XE(0,1)²}

F= {00X:XE(0,1)}

a) (0,1)³=(0,1)×(0,1)×(0,1)

           ={(0,0), (0,1),(1,0),(1,1)} × (0,1)

           ={(0 0 0),(0 0 1),(0,1,0),(0,1,1),(1,0,0),(1,0,1),(1,1,0),(1,1,1)}

A={0,0,0}

B={(1,1,1)}

c={(0,0,0),(0,0,1),(0,1,0),(0,1,1)}

D={(0,1,0),(0,1,1)}

E={(1,0,0),(1,0,1)}

F={(0,0,0),(0,1,0)]

DUE UF is one partition

Since

1)DUEUF= (0,1)³

2)D∩E= E∩F=D∩F=∅

3)D≠∅, E≠∅ and F≠∅

2)CUE is another partition

Since

1) CUE=(0,1)³

2)C∩E =∅

3)C≠∅, E≠∅

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