15. Sets

Try these first

1. 1.

   What is a set?

   Hint

   Think about how elements are grouped.

2. 2.

   What does '∈' signify?

   Hint

   What do we say when we include something in a set?

3. 3.

   What is a set?

   • An ordered collection of objects
   • An unordered collection of objects
   • A collection of only numbers

   Hint

   Think about what makes a collection a set.

4. 4.

   True or False: The empty set and the singleton set containing the empty set are the same.

   • True
   • False

   Hint

   Remember what elements are included in each type of set.

5. 5.

   If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ B, A ∩ B, and A - B?

   Hint

   Use the definitions of union, intersection, and set difference.

6. 6.

   Provide a proof for the statement: For any set A, the power set P(A) has a cardinality of 2^|A|.

   Hint

   Consider how new subsets are formed when each element is added.