Given two sets, determine whether the two sets are equivalent and whether one set is a subset of another. Given one set, determine its power set.

General Information

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

**Grade:**912

**Strand:**Logic and Discrete Theory

**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

Next Benchmarks

### Purpose and Instructional Strategies

In Math for College Liberal Arts, students begin to learn about sets and subsets and their equivalency. In other classes, students will explore additional information about equivalency of sets.- Instruction includes an introduction to sets. A set is a collection of objects. The members of a set are called elements. Sets are represented by capital letters.
- Sets can be described in three ways.
- Word Description:
*W*is the set of days of the week. - Roster Form: elements are listed in { }. The order of the elements does not matter.
*W*= {*Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday*} - Set Builder Notation: {
*x*|*x**________*}.

This is read “the set of all*x*such that*x*is _______.”*W*= {*x*|*x*is a day of the week}

The empty set, or null set, is a set with no elements and can be represented by { } or ∅.

- Word Description:

- Instruction includes defining equivalent sets as sets with the same number of elements
(same cardinality
*n*(*A*) =*n*(*B*)).- Example:

Given set*A*= {*a, b, c, d*} and set*B*= {1,2,3,4} sets A and B are equivalent because both sets have four elements.

- Example:

- Instruction includes defining a subset as a set whose elements are all elements of another
set:
*A*⊆*B*if all elements of A are also in B or there is no element in A that is not in B.- Example:

Given set*A*= {*a, b, c*} and set*B*= {*a, b, c, d*}*A*⊆*B*but*B*?

The empty set is a subset of every set – there is no element in the empty set that is not in the other set.

- Example:

- Students will find the power set of set
*A, P*(*A*) which is defined as the set of all subsets of set A.- Example:

Given*A*= {*a, b*}

The power set is*P*(*A*) = {{ },{*a*},{*b*},{*a, b*}}

- Example:

- Example:

Given*C*= {*red, white, blue*}

The power set is*P*(*C*) = {{ },{*red*},{*white*},{*blue*},{*red, white*},{*red, blue*},{*white, blue*},{*red, white, blue*}}

### Common Misconceptions or Errors

- Students may not include the empty set or the set itself in the power set.

### Instructional Tasks

*Instructional Task 1 (MTR.4.1)*

- Given the following sets:
*A*= {2,4,6, 8,10}*B*= {1,3,5,7,9}*C*= {6,4,8,2}*D*= {*a, b, c, d, e*}*E*= {*a, b, c*}*F*= {10,8,6,4,2}- Part A. Identify the sets that are equivalent to set
*A*. - Part B. Identify the sets that are subsets of
*A*.

- Part A. Identify the sets that are equivalent to set

Instructional Task 2 (MTR.5.1)

Instructional Task 2 (MTR.5.1)

- Part A. Fill in the chart below.

- Part B. How many subsets would you expect there to be for the set

{*red, white, blue, green*}? - Part C. How many subsets would you expect there to be for the set

{*Josh, Abe, Jonah, Allie, Adam, Shane*}? - Part D. Write an equation to represent how many subsets there are for a set of
*n*elements.

### Instructional Items

*Instructional Item 1*

- Find the power set of set
*A*if*A*= {*a, b, c, d*}.

**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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