Set Theory

Sets

1. What is a Set?  Give an example
2. When are two sets equal?  Give an example of two equal sets
3. What is the empty set?  Give an example

And :

True or False

1. True or false. A set is any collection of objects.
2. True or false. A proper subset of a set is itself a subset of the set, but not vice versa.
3. True or false. The empty set is a subset of every set.
4. True or false. If A ∪ B = ∅ , then A =  ∅  and B =  ∅  .
5. True or false. If A ∩ B =  ∅  , then A =  ∅  or B =  ∅  or both A and B are empty sets.
6. True or false. (A ∪ A^c)^c =  ∅  .
7. True or false. [A ∩ (B ∪ C)]^c = (A ∩ B)^c  ∩  (A  ∩  C)^c
8. True or false. n(A) + n(B) = n(A  ∪  B) + n(A  ∩  B)
9. True or false. If A ∈ B, then n(B) = n(A) + n(A^c ∩ B).
10. True or false. The number of permutations of n distinct objects taken all together is n!
11. True or false. P(n, r) = r! C(n, r).