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# 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

Comparing sets

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## 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

• 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.

### Example, are the sets equal?

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

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

### Subsets

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

### Definition

• 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

• In order to show that , we must show that every 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.

### Identifying subsets

• 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

• 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

• , which is true.

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

### Exercise

• Find all the subsets of {1,2,3}

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

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