2. Suppose that A is a set with n (A) = 12. (a) How many dierent subsets does A have? 212 = 4096 (b) How many dierent 11 element subsets does A have?...

2. Suppose that A is a set with n (A) = 12. (a) How many dierent subsets does A have? 212 = 4096 (b) How many dierent 11 element subsets does A have? 12 12 (c) How many dierent 2 element subsets does A have? 3. Suppose that S and T are sets such that n (S) = 21, n (T ) = 17, and n (S [ T ) = 30. n (S T ). 8 4. Let U = fa; b; c; d; e; f; gg ; X = fa; c; e; gg ; Y = fa; b; cg ; and Z = fb; c; d; e; f g. (a) Draw a Venn-diagramm depicting these sets together. (b) Find X Y . X Y = fa; cg (d) Find (X [ Y ) Z: (c) Find X [ (Y Z). (e) How many proper subsets does X [ Y have? 5. How many dierent 6-digit numbers can be formed using the digits 1; 2; 3; 4; 5; 6; 7 and 8; if (a) repetition of digits is allowed?