Section 2.2: Subsets

1 / 8

# Section 2.2: Subsets - PowerPoint PPT Presentation

Section 2.2: Subsets. Objectives Recognize subsets and use the notation ïƒ . Recognize proper subsets and use the notation ïƒŒ. Determine the number of subsets of a set. Subsets.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Section 2.2: Subsets' - zaina

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Section 2.2: Subsets

Objectives

• Recognize subsets and use the notation .
• Recognize proper subsets and use the notation .
• Determine the number of subsets of a set.
Subsets
• Set A is a subset of set B, symbolized A ⊆ B, if and only if all elements of set A are also elements of set B.
• The symbol A ⊆ B indicates that “set A is a subset of set B.”
• The symbol A ⊈ B set A is not a subset of set B.
• To show that set A is not a subset of set B, one must find at least one element of set A that is not an element of set B.
Determining Subsets

Example:

A = { 3, 5, 6, 8 }

B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

• Determine whether set A is a subset of set B.

Solution:

• Determine whether set B is a subset of set A.

Solution:

Proper Subset
• Set A is a proper subset of set B, symbolized A ⊂ B, if and only if all of the elements of set A are elements of set B and set A ≠ B.
• (that is, set B must contain at least one element not is set A).
Determining Proper Subsets

Example:

A = { dog, cat }

B = { dog, cat, bird, fish }

• Determine whether set A is a proper subset of set B.

Solution:

• Determine whether set B is a proper subset of set A.

Solution:

Determining Proper Subsets

Example:

Determine whether set A is a proper subset of set B.

A = { dog, bird, fish, cat }

B = { dog, cat, bird, fish }

Solution:

Number of Distinct Subsets

The number of distinct subsets of a finite set A is 2n, where n is the number of elements in set A.

Example:

• Determine the number of distinct subsets for the given set {t, a, p, e}.
• List all the distinct subsets for the given set {t, a, p, e}.
Number of Distinct Proper Subsets

The number of distinct proper subsets of a finite set A is 2n– 1, where n is the number of elements in set A.

Example:

Determine the number of distinct proper subsets for the given set{t, a, p, e}.

Solution: