Finite Math

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 ∪ Ac)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(Ac ∩ 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).
12. True or false. If E and F are mutually exclusive, and E and G are mutually exclusive, then F and G are mutually exclusive.
13. True or false. Suppose it is determined that the probability of obtaining heads in a coin- tossing experiment using a biased coin is 0.51, then the probability of obtaining tails in a toss of the coin is 0.49.
14. True or false. Suppose S = {s1, s2, …, sn} is a finite sample space with n outcomes. Then 0 < P(s1) + P(s2) + … + P(sn) < 1.
15. True or false. P(E) + P(Ec) = 1.
16. True or false. P(Ec ∪ Fc) = 1 – P(E ∩ F)