Question

Please help it's due tomorrow ​

Answer 1

C. {1, 2, 4, 6, 7, 8, 10}

Explanation:

Given sets:

• 
  `\text{U}=\n`

• 
  `A=\{3,4,5,7,8\}`

• 
  `B=\{2,4,6,8,10}`

"Z" represents the set of all integers. An integer is a whole number (not a fractional or decimal number) that can be positive, negative, or zero.

Therefore, the universal set is:

• U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A' means the complement of set A.

The complement of a set refers to all the elements that are not in the given set. So in this context, elements that are in the universal set but not in set A. Therefore:

• A' = {1, 2, 6, 9, 10}

The symbol ∪ represents the union of sets.

The union of two sets is a new set that contains all the elements that are in either set or in both sets.

Solution

`\begin{aligned}\sf A' \cup B&=(\text{U}-A) \cup B\\&=\left(\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}-\{3,4,5,7,8\}\right) \cup \{2,4,6,8,10\}\\&=\{1, 2, 6, 9, 10\} \cup \{2,4,6,8,10\}\\&=\{1, 2, 4, 6, 8, 9, 10\}\end{aligned}`

`\hrulefill`

Set Notation:

`\begin{array}l \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}`