Math Problem Statement

Diketahui himpunan A yaitu A = {2, 4, 6, 8} dan himpunan semesta S = {10, 12, 14, 16, 18, 20}. Tentukanlah hasil dari himpunan A dikomplemenkan!

Solution

The image shows an example problem related to set theory in Indonesian, specifically focusing on the complement of a set. Here's a translation and breakdown of the problem:


Example:

Given the set AA, which is:
A={2,4,6,8}A = \{2, 4, 6, 8\}

and the universal set SS, which is:
S={10,12,14,16,18,20}S = \{10, 12, 14, 16, 18, 20\}

Determine the complement of set AA!

Solution:

Since there are no elements of set AA within the universal set SS, the complement of set AA, denoted by AcA^c, is:
Ac={10,12,14,16,18,20}A^c = \{10, 12, 14, 16, 18, 20\}.


In summary, the complement of set AA in this case is the set of elements in SS that are not in AA.


Do you have any questions about this, or would you like further details?

Here are 5 follow-up questions to expand on this concept:

  1. How do we determine the complement of a set in general?
  2. Can a set have multiple complements depending on the universal set?
  3. What happens if set AA shares some elements with the universal set SS?
  4. How would we express the complement of AA using set notation?
  5. How do we apply the concept of set complements in real-world problems?

Tip: Always define the universal set clearly before determining the complement of any set.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Complement of a Set

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9