Represent logic operations, such as AND, OR, NOT, NOR, and XOR, using logical symbolism to solve problems.

General Information

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**912

**Strand:**Logic and Discrete Theory

**Standard:**Develop an understanding of the fundamentals of propositional logic, arguments and methods of proof.

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## Benchmark Instructional Guide

### Connecting Benchmarks/Horizontal Alignment

### Terms from the K-12 Glossary

### Vertical Alignment

Previous Benchmarks

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### Purpose and Instructional Strategies

In Math for College Liberal Arts, students represent logical operations, such as AND, OR, NOT, NOR, and XOR, using logical symbolism to solve problems involving classifying items as belonging to sets.- This benchmark builds on MA.912.LT.4.1 and MA.912.LT.4.2 as it involves representing or translating statements using logical connectives or operations, as well as determining the truth value of an output given the truth value of the inputs.
- Instruction includes defining of the logic operations as functions.

- Operators may be in capital or lower case letters. Instruction progresses from using all capital letters to lower case letters in order to ensure students recognize the operators.
- Instruction includes connections to set operations and Venn Diagrams (MA.912.LT.5.4
and MA.912.LT.5.5) using real-world contexts such as choosing the appropriate logic
operation and writing a search query to identify a subset of a population.
- For example, suppose
*R*is the set of all romance books, and*T*is the set of all true crime books in a library database.

- For example, suppose

- All the books that are an element of the set
*R*.

- All the books that are both a romance and a true crime, which is the
intersection of
*R*and*T*.

- All the books that are a romance, a true crime, or both, which is the union
of
*R*and*T*. This is the inclusive or.

- All the books that are not a true crime, which is the complement of
*T*.

- All the books that are not a true crime and not a romance, which is the
complement of the union of
*R*and*T*.

- All the books that are a true crime or a romance, but not both. This is the union minus the intersection, which is the exclusive or.
- Instruction directs students to decide whether an element is a member of resulting set
given the conditions and logic operations (MTR.6.1).
- For example, if given a book that is a true crime romance, students would determine to which of the operator(s) AND, OR, NOT, NOR or XOR it belongs.
- For example, if given an operator of NOT, does the true crime romance book belong to that set.

- Students also engage in discussions with their peers, analyzing the mathematical thinking of others (MTR.4.1), demonstrating their understanding by representing their reasoning in multiple ways (e.g., Venn Diagram, set operations, specific examples of set elements).
- Instruction mentions that logic operators are used in Boolean Algebra, logic gates and
computer science topics.
- Boolean Algebra focuses on binary variables with truth values being coded as a 0 or 1.
- Logic Gates is the visualization model of Boolean Algebra. Logic gates can be a device that acts as building blocks for digital circuits.

### Common Misconceptions or Errors

- Students may use the logic operation OR as ‘exclusive or.’ To help address this, make
connection to the set operation of the union to reinforce the meaning of ‘
*p*OR*q*’ as ‘*p*or*q*or both*p*AND*q*.’ - Students may use the logic operation AND to join two sets. To help address this, make connection to the set operation of the intersection.

### Instructional Tasks

*Instructional Task 1 (MTR.1.1, MTR.4.1)*

- Work with a partner(s) to determine the set of numbers that meet these conditions as a whole.
- Part A. What are some examples of numbers that meet the condition “NOT an odd number?”
- Part B. What are some examples of numbers that meet the condition “less than 20 AND greater than 1?”
- Part C. What are some examples of numbers that meet the condition “multiple of 3 OR multiple of 5?”
- Part D. Describe the numbers that meet the following conditions: NOT an even number AND less than 20 AND greater than 1 AND (multiple of 3 OR multiple of 5).

### Instructional Items

*Instructional Item 1*

- Suppose your high school has a database of all students along with many characteristics of each student such as name, current grade level, intended career path, and many others. A segment of the student characteristics table is shown.

- Which of the following search queries would generate the list of 12th graders, on a Business
Career Path?
- a. Grade_Level is 12 AND Career_Path is Business
- b. Grade_Level is greater than 11 OR Career_Path is Business
- c. Grade_Level is NOT 9 AND Grade_Level is NOT 10 AND Grade_Level is NOT 11 AND Career_Path is Business
- d. Grade_Level is 12 AND Career_Path is NOT STEM

**The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.*

## Related Courses

This benchmark is part of these courses.

7912070: Access Mathematics for Liberal Arts (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 - 2023, 2023 and beyond (current))

1207350: Mathematics for College Liberal Arts (Specifically in versions: 2022 and beyond (current))

1212300: Discrete Mathematics Honors (Specifically in versions: 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

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