Math Problem Statement

Let U​ = { 6​, 7​, 8​, 9​, 10​, 11​, 12 ​}, A​ = { 8​, 10​, 11​, 12 ​}. Use the roster method to write the set Upper A prime. Question content area bottom Part 1 Upper A primeequalsStartSet nothing EndSet

​(Use a comma to separate answers as​ needed.)

Solution

To find AA' (the complement of set AA relative to set UU), we need to identify all the elements in the universal set UU that are not in AA.

Given:

  • U={6,7,8,9,10,11,12}U = \{6, 7, 8, 9, 10, 11, 12\}
  • A={8,10,11,12}A = \{8, 10, 11, 12\}

The complement of AA, denoted AA', consists of the elements in UU that are not in AA.

By inspection:

  • U={6,7,8,9,10,11,12}U = \{6, 7, 8, 9, 10, 11, 12\}
  • A={8,10,11,12}A = \{8, 10, 11, 12\}

So, the elements that are in UU but not in AA are 6,7,6, 7, and 99.

Thus, A={6,7,9}A' = \{6, 7, 9\}.

Final Answer:

A={6,7,9}A' = \{6, 7, 9\}


Would you like further clarification on this or have any questions about set complements?

Here are some related questions:

  1. How do you find the union of two sets?
  2. What is the difference between a set and a subset?
  3. How do you determine the intersection of two sets?
  4. What is the power set of a given set?
  5. How do you express the complement of a set with respect to a larger set?

Tip: When finding the complement of a set, always remember that you're looking for elements in the universal set that aren't part of the specific set you're working with.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Set Complements
Roster Method

Formulas

A' = U - A

Theorems

Complement of a set

Suitable Grade Level

Grades 6-8