---
title: "AFM.LR.3: Logical Arguments and Reasoning (Georgia Mathematics standard)"
code: AFM.LR.3
cite_as: Georgia Standards of Excellence, Mathematics, AFM.LR.3
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/AFM.LR.3
md_url: https://georgiahomeroom.org/standards/code/AFM.LR.3.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/AFM.LR.3.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.LR.3: Logical Arguments and Reasoning

Interpret, represent, and communicate logical arguments to explain reasoning and justify thinking when solving problems and to explain real-life phenomena.

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

## Expectations

- Represent and interpret statements using logical symbolism.
  - **AFM.LR.3.1**: Construct truth tables that represent conditional, biconditional, and quantified statements; use truth tables to determine whether the statement is true or false and use Venn diagrams to illustrate the relationship represented by these truth tables.
  - **AFM.LR.3.2**: Represent logic operations such as AND, OR, NOT, NOR, and XOR (exclusive OR) using logical symbolism, determine whether statements involving these operations are true or false, and interpret such symbols into English.
  - **AFM.LR.3.3**: Apply modus ponens and modus tollens to analyze logical arguments to determine whether it is valid, invalid, a tautology, or a contradiction.
  - **AFM.LR.3.4**: Write the negation, converse, contrapositive, and inverse of a conditional statement and find the truth of each.
- Use binary to represent and interpret logical statements.
  - **AFM.LR.3.5**: Represent the dichotomy between “true” and “false” with 1s and 0s. Use 1s and 0s to calculate whether a statement is true or false by constructing Boolean logic circuits.
  - **AFM.LR.3.6**: Convert binary and hexadecimal numbers into decimal, and convert from binary to hexadecimal, and vice versa. Add binary integers and use 2’s complement to subtract binary integers.

## 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.