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 bothA ;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).