Question

Algebra: Determine the intersection, union, and complement sets from the given information. (ITS URGENT)

Answer 1

1. a) A ∩ B = {1}

1. b) A ∪ B = {0, 1, 2, 3}

1. c) B' = {0, -1}

2. a) A ∩ B = ∅

2. b) A ∪ B = {4, 5, 6, 7, 8, 9}

2. c) (A ∪ B)' = {10}

3. a) A ∩ B = ∅

3. b) A ∪ B = {4, 5, 6}

3. c) A' = {5, 6, 7}

Explanation:

Set Notation

The symbol
`\text{U}` is used to represent the universal set. The universal set contains all the elements under consideration.

The symbol ∩ is used to represent the intersection of sets. The intersection of two sets refers to the set that contains only the elements that are common to both sets.

The symbol ∪ represents the union of sets. The union of two sets is a set that includes all the elements that are present in either of the two sets, or in both sets.

The symbol ' represents the complement of a set. The complement of a set refers to the set that contains all the elements that are not present in the original set but are part of the universal set.

The symbol ∅ or { } represents an empty set. The empty set does not contain any elements.

`\hrulefill`

Question 1

Given sets:

• U = {-1, 0, 1, 2, 3}
• A = {0, 1}
• B = {1, 2, 3}

`\begin{aligned} \textsf{a)}\quad \sf A \cap B&=\{0,1\} \cap \{1, 2, 3\}\\&=\{1\}\end{aligned}`

`\begin{aligned} \textsf{b)}\quad \sf A \cup B&=\{0,1\} \cup \{1, 2, 3\}\\&=\{0,1,2,3\}\end{aligned}`

`\begin{aligned} \textsf{c)}\quad \sf B'&=\sf \text{U}-B\\&=\{-1, 0, 1, 2, 3\}-\{1, 2, 3\}\\&=\{0,-1\}\end{aligned}`

`\hrulefill`

Question 2

Given sets:

• U = {4, 5, 6, 7, 8, 9, 10}
• A = {7, 8, 9}
• B = {4, 5, 6}

`\begin{aligned} \textsf{a)}\quad \sf A \cap B&=\{7, 8, 9\} \cap \{4, 5, 6\}\\&=\emptyset \end{aligned}`

`\begin{aligned} \textsf{b)}\quad \sf A \cup B&=\{7, 8, 9\} \cup\{4, 5, 6\}\\&=\{4, 5, 6,7,8,9\}\end{aligned}`

`\begin{aligned} \textsf{c)}\quad \sf (A \cup B)'&=\sf \text{U}-(A \cup B)\\&=\{4, 5, 6, 7, 8, 9, 10\}-\{4, 5, 6,7,8,9\}\\&=\{10\}\end{aligned}`

`\hrulefill`

Question 3

Given sets:

• U = {4, 5, 6, 7}
• A = {4}
• B = {5, 6}

`\begin{aligned} \textsf{a)}\quad \sf A \cap B&=\{4\} \cap \{5,6\}\\&=\emptyset\end{aligned}`

`\begin{aligned} \textsf{b)}\quad \sf A \cup B&=\{4\} \cup\{5,6\}\\&=\{4,5,6\}\end{aligned}`

`\begin{aligned} \textsf{c)}\quad \sf A'&=\sf \text{U}-A\\&=\{4, 5, 6, 7\}-\{4\}\\&=\{5,6,7\}\end{aligned}`