Question

List all of the proper subsets of the set a = 1, 8?

Answer 1

The proper subsets of the set a = {1, 8} are the empty set, {1}, and {8}. A proper subset contains fewer elements than the original set, and thus the set itself is not included.

Step-by-step explanation:

Proper Subsets of a Set

Given the set a = {1, 8}, the proper subsets are all the subsets of a that do not contain all the elements of a. Therefore, the list of all proper subsets is:

• 
  
• { }
• 
  
• {1}
• 
  
• {8}

The empty set, denoted by { }, is a proper subset of any set because it does not contain any elements. Each single element of the set is also a proper subset since they contain fewer elements than the original set. The set consisting of both elements, {1, 8}, is not a proper subset because it is exactly the same as the original set a.