Question 1# For universal set U = {a,b,c,...,} (the alphabet) let V be the set of...
Let the Universal set be the letters a through j: U = {a, b, ..., i, j}. Let A = {a, c, e, i}, B = {a, b, e, g), and C = {a, b, f, i} List the elements of the set An (BUC)
. Let A, B and C be subset of a universal set U. (a) Prove that: Ac x Bc ⊂ (A × B)c (the universal set for A × B is U × U). So A compliment x B compliment = AxB Compliment
discrete math '-(oe : length(a) 29, be the alphabet {a,b,c,d,e,f,g) and let 7. Let a) How many elements are in the following set? {ωΣ: no letter in ω is used more than once) b) Find the probability that a random word we has al distinct letters. e) Find the probability that a random word oe has the letter g used exactly once. d) Find the probability that a random word e does not contain the letter g. '-(oe : length(a)...
11. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: A ∪ B 12. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: b. A ∩ B 13. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g} and B = {d, e, f, g}. Find: AC...
8. Let A and B be subsets of some universal set U. From Proposition 5.10, we know that if A S B, then B S A. Now prove the following proposition: For all sets A and B that are subsets of some universal set U, A C B if and only if B S A.
D Question 7 Let A and B be subsets of a universal set U with n (U)-32, n (A) = 11, n (B) = 17, and n (AUB) = 25. Compute n(A' nB) D Question 8 Let A and B be subsets of a universal set U with n (U)-32, n (A)-11, n (B)-17, and n (A U B)=25 Compute n (AUB).
A,C,G please 1. Let A, B, and C be subsets of some universal set u. Prove the following statements from Theorem 4.2.6 (a) AUA=/1 and AnA=A. (b) AUO- A and An. (c) AnB C A and ACAUB (d) AU(BUC)= (A U B) U C and An(B n C)-(A n B) n C. (e) AUB=BUA and A n B = B n A. (f) AU(BnC) (AU B) n(AUC) (g) (A U B) = A n B (h) AUA=1( and An-=0. hore...
6. Let A, B, and C be subsets of some universal set U. Prove or disprove each of the following: * (a) (A n B)-C = (A-C) n (B-C) (b) (AUB)-(A nB)=(A-B) U (B-A) 6. Let A, B, and C be subsets of some universal set U. Prove or disprove each of the following: * (a) (A n B)-C = (A-C) n (B-C) (b) (AUB)-(A nB)=(A-B) U (B-A)
c) Definition: Let A and B be two sets (within some universal set X) A and be are called disjoint if A n B 0. 15 pts. Prove the following. A and B are disjoint if and only if A/B-A U B
2. Let A-(2, 3, 4), B = {3, 4, 5, 6), and suppose the universal set is U-(1,2 all the elements in the following sets. ,9). List (a) (A U B) (b) (ANB) × A (c) P(An B)