15.3. Special Sets

Try these first

1. 1.

   What is the empty set?

   Hint

   Think of a bag with nothing inside.

2. 2.

   Give an example of a singleton set.

   Hint

   A set with just one item can be a singleton.

3. 3.

   What does the symbol ϕ represent?

   • A singleton set
   • The empty set
   • A proper subset

   Hint

   Recall what an empty set indicates.

4. 4.

   True or False: The empty set is equal to {ϕ}.

   • True
   • False

   Hint

   Think about the elements each set contains.

5. 5.

   Prove that the empty set is a subset of any set A, using logic and definitions.

   Hint

   Think about how subset definitions work.

6. 6.

   Create examples of sets A, B, C such that A is a proper subset of B, and both sets include a singleton set.

   Hint

   What makes one a proper subset.