Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} be the universal set. Consider the two subsets A = {0, 2, 4, 6, 8} and B = {0,3,6,9}. Use the roster method to write each of the following sets (a) AUB. (b) An B. (c) AC. (d) (AUB) – AC
Please help me prove 2,4, and 5. Thank you Theorem 17. Let A, B and C be sets. Then the following statements are true: (1) AB CA; (2) B CAUB; (3) A CAUB; (4) AB=BA; (5) AU (AUC) = (AUB) UC; (6) An(BNC) = (ANB) nC; (7) An (BUC) = (ANB) U (ANC); (8) AU (BAC) = (AUB) n(AUC).
3. (7pts). Let S ,2, 3, 4, 5, 6, 7, 8, 9, 10 be our Sample space and A 1,2, 3, 4, 5, 6) and B Calculate the sets of: 5, 6, 7, 8, 9) be two sets of elements ofS AUB (AUB) (AnB)
Q1 lf S-(Q 1, 2, 3, 4, 5, 6, 7, 8, 9} and A-|0, 2, 4, 6, 8], B (1, 3, 5, 7, 9), C (2, 3, 4, 5), and D [1,6,7], list the elements of the sets corresponding to the following events: (a) A U C; (b) An B; (d) (C' n D) U B; (e) (s n c)' (f) Anc n D'.
0 Q1 D lf S- {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and A-|0, 2, 4, 6, 8], B (1, 3, 5, 7,9), С (2, 3, 4, 5), and [1,6,7], list the elements of the sets corresponding to the following events: (a) A U C; (b) A n B; (d) (C' n D) U B; (e) (s n c)' (f) Anc n D'.
Let U = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10), A = (1, 3, 5, 7, 9), 8 (2, 4, 6, 8, 10), and C (1, 2, 3, 4, 5, 10). List the elements of each set. (Enter your answers using roster notation. Enter EMPTY or for the empty set.) (a) 4 {2, 4, 6, 8, 10) (Đ) 1 0 0 {2,4, 10) X (1) cuc {}
(2) Find their intersection and union: Let A={1,3,5,7,9}, B = {2, 4, 6, 8, 10}, C = {1,2,3,4,5}, (2a) (a) AnB =? (2b (b) AnC =? (c) AUB=? (2c). (d) AUC =? (20) (4) Express the following compound inequality: * <4 AND 3-1 (a) in set-builder notation:) (4a) (b) (graph it on the number line:) - -3 3 (c) (in interval notation:) (4c) (3) Answer the following questions: (if A and B are two sets) (a) (The keyword AND A...
Let A = {1, 2}, B = {3, 5, 6}, C = {1, 2, 3, 5, 7}, D = {4, 7, 9}, and U = {1, 2, 3, . . . , 9, 10}. 1. Find B ∪ C. 2. Find B ∩ C. 3. Find A ∪ B. 4. Find C ∩ D. 5. Find C'. 6. Find B'. 7. Is 4 ∈ C? 8. Is B ⊆ C? 9. Is A ⊆ C? 10. Are A and B...
9. Let f be the following permutation in the symmetric group S9, written in two-line notation. 1 2 3 4 5 6 7 8 9 5 9 4 8 2 6 1 3 7 (a) Determine f3121 and explain why your answer is correct. (b) Determine ord(f) (c) Find a permutation p such that p-f 9. Let f be the following permutation in the symmetric group S9, written in two-line notation. 1 2 3 4 5 6 7 8 9...
Exercise 3.5. Let A 3,8), and B 2, 6, C (With of course Ω-R) Find the following: (5, 0o), and D (-oo,3 a AUB, An B, and Bn b A, AU D, and An D