15.9. Proving Set Identities

Try these first

1. 1.

   Define what it means for two sets to be equal.

   Hint

   Think about element presence!

2. 2.

   What does De Morgan's Law state?

   Hint

   Remember the complement and the two operations involved!

3. 3.

   Which of the following statements about sets is true?

   • A = B if A ⊆ B and B ⊆ A
   • A = B if A ∩ B is non-empty
   • A = B if A ∪ B = A

   Hint

   Focus on definitions of subsets.

4. 4.

   Do De Morgan's Laws result in equal sets?

   • True
   • False

   Hint

   Recall what happens with complements!

5. 5.

   Demonstrate that if A = {1, 2, 3} and B = {3, 4, 5}, then show A ∩ (A ∪ B) = A.

   Hint

   Dissolve both sides to see the content!

6. 6.

   Prove that if A ⊆ B and B = C, then A = C.

   Hint

   Think about how sets relate!