15.6. Power Set

Try these first

1. 1.

   What is the power set of an empty set?

   Hint

   Remember that the only subset of the empty set is the empty set itself.

2. 2.

   How many subsets are there in the set {1, 2, 3}?

   Hint

   Use the formula 2^n, where n is the number of elements.

3. 3.

   What is the power set of {1, 2}?

   • {1
   • 2}
   • {1
   • 2
   • 3}
   • {}
   • {1}
   • {2}
   • {1
   • 2}

   Hint

   Think about every possible combination.

4. 4.

   True or False: The power set of a set with 3 elements has 6 subsets.

   • True
   • False

   Hint

   Use the power set formula.

5. 5.

   Given the set S = {a, b, c, d}, how many distinct subsets can be formed? Prove your answer using the power set formula.

   Hint

   Break down each element's contributions to subsets.

6. 6.

   Explain in detail how the inductive proof works for the statement about power sets.

   Hint

   Remember to express the subsets clearly and summarize logically.