1 / 10

# Comparing sets - PowerPoint PPT Presentation

Comparing sets. Chapter 2 Sec 2. Set equality. One of the fundamental things we need to know about two sets is when do we consider them to be the same. Def

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

## PowerPoint Slideshow about ' Comparing sets' - mills

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

### Comparing sets

Chapter 2 Sec 2

• One of the fundamental things we need to know about two sets is when do we consider them to be the same.

• Def

• Two sets A and B are equal if they have exactly the same members. In this case, we write A = B. If A and B are not equal, we write A ≠ B.

• {Socrates, Shakespeare, Armstrong} = {Armstrong, Socrates, Shakespeare}

• A={x:x is a citizen of the US} and B={y:y was born in the US}

• Another way we compare sets is to determine whether one set is part of another set.

• The set A is a subset of the set B if every element of A is also an element of B. We indicate this relationship by writing . If A is not a subset of B, then we write

Identifying subsets element of A also occurs as an element of B. To show that A is not a subset of B, all we have to do is find one element of A that is not in B.

• Determine whether either set is a subset of the other.

• A ={2, 5, 6} and B ={1,2, 5, 6}

• Every member of A is in B, therefore we can write .

• But, there is an element of B that is not in A,

Proper Subset element of A also occurs as an element of B. To show that A is not a subset of B, all we have to do is find one element of A that is not in B.

• The set A is a proper subset of the set B if but A ≠ B.

• We write this as .

• If A is not a proper subset of B, then we write

Example element of A also occurs as an element of B. To show that A is not a subset of B, all we have to do is find one element of A that is not in B.

• , which is true.

• Also because {1,2,3,…} contains elements that are not members of {2,4,6,…}.

Exercise element of A also occurs as an element of B. To show that A is not a subset of B, all we have to do is find one element of A that is not in B.

• Find all the subsets of {1,2,3}

• If a set has five elements, how many subsets will it have?

• 25