---
title: "AFM.AQR.5: Set Theory Applications (Georgia Mathematics standard)"
code: AFM.AQR.5
cite_as: Georgia Standards of Excellence, Mathematics, AFM.AQR.5
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/AFM.AQR.5
md_url: https://georgiahomeroom.org/standards/code/AFM.AQR.5.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/AFM.AQR.5.md
source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180
source_last_changed: 2024-10-09
data_built: 2026-09-18
publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district.
up: https://georgiahomeroom.org/standards/math/high-school.md
index: https://georgiahomeroom.org/standards/index.md
---

# AFM.AQR.5: Set Theory Applications

Use set theory to describe relationships and equivalence when solving contextual, mathematical problems used to explain real-life phenomena.

- Subject: Mathematics
- Appears in: High School, https://georgiahomeroom.org/standards/math/high-school.md

## Expectations

- Use set theoretic operations.
  - **AFM.AQR.5.1**: Find the union, intersection, difference, complement, and Cartesian product of sets, and classify sets as equal, subsets, and power sets.
  - **AFM.AQR.5.2**: Justify whether the union of subsets of a set is a partition of that set.
  - **AFM.AQR.5.3**: Given a relation on two sets, determine whether the relation is a function and find its inverse relation, if it exists.
  - **AFM.AQR.5.4**: Determine the equivalence classes given an equivalence relation on a set; determine whether the union of equivalence classes of a set is a partition of that set.
  - **AFM.AQR.5.5**: Prove set relations, including DeMorgan’s Laws and equivalence relations.
- Use and interpret Boolean algebra.
  - **AFM.AQR.5.6**: Prove statements in Boolean algebra.
  - **AFM.AQR.5.7**: Simplify Boolean algebra expressions using Karnaugh maps (K-maps).

## Georgia Milestones coverage

No Georgia Milestones blueprint cites this standard.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.