1. Chapter 2 Sec 2

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.

3.  {Socrates, Shakespeare, Armstrong} = {Armstrong, Socrates, Shakespeare}  A={x:x is a citizen of the US} and B={y:y was born in the US}

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

5.  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

6.  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.

7.  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,

8.  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

9. , which is true.  Also because {1,2,3,…} contains elements that are not members of {2,4,6,…}.

10.  Find all the subsets of {1,2,3}  If a set has five elements, how many subsets will it have? 2525