15.8. Set Identities

Try these first

1. 1.

   What is the cardinality of the set {3, 1, 2}?

   Hint

   Count the elements in the set.

2. 2.

   Is {x} a singleton set?

   Hint

   Think about the definition of a singleton set.

3. 3.

   What does A ∩ B represent?

   • Elements in A only
   • Elements in B only
   • Elements common to both A and B

   Hint

   Look for common elements in both sets.

4. 4.

   True or False: The power set of {1, 2} contains 4 elements.

   • True
   • False

   Hint

   Consider the subsets of a 2-element set.

5. 5.

   Given sets A = {1, 2, 3}, B = {3, 4, 5}, and C = {1, 4}, prove that A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C).

   Hint

   Think about the distributive property of sets.

6. 6.

   Construct the power set of the set D = {a, b}. List all subsets and explain.

   Hint

   Consider how many subsets you can form from 2 elements.