3. Let $$ A=\{1,2,3,4,5\}, B=\{2,4,6\}, C=\{3,4,5\} $$ and let $$ E=\{0,1,2,3,4,5,6,7,8\} $$ Find $$ \begin{array}{lllll} ext { i) } B^{\prime} & ext { ii) } A \cup B & ext { iii) } A \cap B & ext { iv) }(A \cup B)^{\prime} & ext { v) }(A \cap B)^{\prime}\end{array} $$ vi) $$ C-B $$

Question

3. Let $$ A=\{1,2,3,4,5\}, B=\{2,4,6\}, C=\{3,4,5\} $$ and let $$ E=\{0,1,2,3,4,5,6,7,8\} $$ Find $$ \begin{array}{lllll}	ext { i) } B^{\prime} & 	ext { ii) } A \cup B & 	ext { iii) } A \cap B & 	ext { iv) }(A \cup B)^{\prime} & 	ext { v) }(A \cap B)^{\prime}\end{array} $$ vi) $$ C-B $$

UpStudy AI · Accepted Answer

Let's analyze each part step-by-step using the given sets:

- **Universal Set $$ E $$:** $$\{0,1,2,3,4,5,6,7,8\}$$
- **Set $$ A $$:** $$\{1,2,3,4,5\}$$
- **Set $$ B $$:** $$\{2,4,6\}$$
- **Set $$ C $$:** $$\{3,4,5\}$$

### i) $$ B' $$ (The complement of $$ B $$ in $$ E $$)
The complement of $$ B $$ consists of all elements in $$ E $$ that are **not** in $$ B $$.

$$
B' = E - B = \{0,1,3,5,7,8\}
$$

### ii) $$ A \cup B $$ (The union of $$ A $$ and $$ B $$)
The union includes all elements that are in $$ A $$ **or** $$ B $$, without duplicates.

$$
A \cup B = \{1,2,3,4,5,6\}
$$

### iii) $$ A \cap B $$ (The intersection of $$ A $$ and $$ B $$)
The intersection includes only the elements that are in **both** $$ A $$ and $$ B $$.

$$
A \cap B = \{2,4\}
$$

### iv) $$ (A \cup B)' $$ (The complement of $$ A \cup B $$ in $$ E $$)
This includes all elements in $$ E $$ that are **not** in $$ A \cup B $$.

$$
(A \cup B)' = E - (A \cup B) = \{0,7,8\}
$$

### v) $$ (A \cap B)' $$ (The complement of $$ A \cap B $$ in $$ E $$)
This includes all elements in $$ E $$ that are **not** in $$ A \cap B $$.

$$
(A \cap B)' = E - (A \cap B) = \{0,1,3,5,6,7,8\}
$$

### vi) $$ C - B $$ (The set difference of $$ C $$ and $$ B $$)
This includes all elements that are in $$ C $$ but **not** in $$ B $$.

$$
C - B = \{3,5\}
$$

**Summary of Results:**

i) $$ B' = \{0,1,3,5,7,8\} $$  
ii) $$ A \cup B = \{1,2,3,4,5,6\} $$  
iii) $$ A \cap B = \{2,4\} $$  
iv) $$ (A \cup B)' = \{0,7,8\} $$  
v) $$ (A \cap B)' = \{0,1,3,5,6,7,8\} $$  
vi) $$ C - B = \{3,5\} $$
i) $$ B' = \{0,1,3,5,7,8\} $$ ii) $$ A \cup B = \{1,2,3,4,5,6\} $$ iii) $$ A \cap B = \{2,4\} $$ iv) $$ (A \cup B)' = \{0,7,8\} $$ v) $$ (A \cap B)' = \{0,1,3,5,6,7,8\} $$ vi) $$ C - B = \{3,5\} $$

Let and let
Find vi)

Upstudy AI Solution

Answer

Solution

i) (The complement of in )

ii) (The union of and )

iii) (The intersection of and )

iv) (The complement of in )

v) (The complement of in )

vi) (The set difference of and )

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