I have to make a true statement with this question:
{All states west of the Rocky Mountains}
{All states west of the
Atlantic Ocean}
I have to determine if the two statements are:
Proper Subset
is a subset of
is not a subset of
proper subset and is a subset of
Since this is not my area of expertise, I searched Google under the key words "proper subsets" to get this:
http://en.wikipedia.org/wiki/Subset
http://mathworld.wolfram.com/ProperSubset.html
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search. Also see http://hanlib.sou.edu/searchtools/.
To determine the relationship between the two statements, "All states west of the Rocky Mountains" and "All states west of the Atlantic Ocean," we need to analyze their relationship in terms of subsets.
First, let's define what these two sets represent. The set "All states west of the Rocky Mountains" includes states such as California, Oregon, and Washington, among others. On the other hand, the set "All states west of the Atlantic Ocean" includes states like Illinois, Texas, and Arizona, among others.
Now, let's examine their relationship:
1. Proper Subset: A set A is a proper subset of set B if every element of A is also an element of B, but B contains at least one element that is not in A.
Based on this definition, neither statement is a proper subset of the other because they contain different elements. The states west of the Rocky Mountains are not necessarily the same states as those west of the Atlantic Ocean, and vice versa.
2. Subset: A set A is a subset of set B if every element of A is also an element of B.
Using this definition, neither statement is a subset of the other because they have different elements. The set of states west of the Rocky Mountains does not include all the states west of the Atlantic Ocean, and vice versa.
3. Is not a subset of: This is similar to the subset relationship, but it indicates that at least one element of A is not in B.
Since the two statements have different elements, neither is a subset of the other.
4. Proper subset and is a subset of: The proper subset relationship is already defined as a subset where B contains at least one element not in A. Since neither statement is a subset of the other, they cannot be proper subsets either.
To summarize, the two statements are neither proper subsets, subsets, nor proper subset and a subset of each other. They represent geographically distinct regions and, therefore, have no inherent subset relationship.