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
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.
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,
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
, which is true. Also because {1,2,3,…} contains elements that are not members of {2,4,6,…}.
Find all the subsets of {1,2,3} If a set has five elements, how many subsets will it have? 2525