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1. A universal set, with n(U)70, is partitioned into three subsets: A, B, and C. If...
1. Let U be the universal set with disjoint subsets A and B, where n(U-46, n(A-15,...
1. Let U be the universal set with disjoint subsets A and B, where n(U-46, n(A-15, and n(B-14. Find nAn B 2. A merchant surveyed 300 people to determine the way they leaned about an upcoming sale. The survey showed that 180 learned about the sale from the radio, 170 from television, 130 from the newspaper, 120 from radio and television, 70 from radio and newspapers, 80 from television and newspapers, and 60 from all three sources. How many people...
D Question 7 Let A and B be subsets of a universal set U with n...
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).
Let A, B, and be subsets of a universal set U and suppose n(U) - 200,...
Let A, B, and be subsets of a universal set U and suppose n(U) - 200, n(A) -21, n(B) = 23, (C) -27, [ AB) - 7, n(ANC) - 10, n(BC) - 13, and ( ABN) - 3. Compute: (a) MAN (BUCI (b) AN (BU09
6. Let A, B, and C be subsets of some universal set U. Prove or disprove each of the following: *...
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)
A,C,G please 1. Let A, B, and C be subsets of some universal set u. Prove...
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...
5. Let A, B, C be subsets of a universal set U. Recall for D CU...
5. Let A, B, C be subsets of a universal set U. Recall for D CU that XD denotes the characteristic function of D. Prove that XAUBUC = XA +XB+XC - XAMB - XAOC · XBNC + XANBNC. Hint: Facts that you may use: (1) Xpe = 1 – Xd. (2) (AU BUC)° = A n Bºn Cº. (3) XEnF = XEXF. (4) XEnFnG XEXFXG. Don't prove these facts.
1. Let S and T be subsets of the universal set U. Use the Venn diagram...
1. Let S and T be subsets of the universal set
U. Use the Venn diagram on the right and the given data below to
determine the number of elements in each basic region.
n(U)=25
n(S)=13
n(T)=14
n(SUT)=19
Region I contains _____ elements
Region II contains _____ elements
Region III contains _____ elements
Region IV contains _____ elements
______________________________________________________________________________________________________
2. Let R, S, and T be subsets of the universal
set U. Use the Venn diagram on the right and...
Question 1# For universal set U = {a,b,c,...,} (the alphabet) let V be the set of...
Question 1# For universal set U = {a,b,c,...,} (the alphabet) let V be the set of all letters used in the name "Vincent Van Gogh" and let W be the set of letters used in the word "watercolourist". How many members have each of the following sets? Show your enumeration calculation. (a) V (b) VW () VAW (c) VUW (f) P(V) (the power set of V] (d) V W
(a) We want to select three subsets A, B, and C of [n] so that A...
(a) We want to select three subsets A, B, and C of [n] so that A -C and B C C. How many ways can this be done? (b) We want to select three subsets A, B, and C of [n so that ACC, BC C, and An BメØ. How many ways can this be done?
11. Let the universal set be the set U = {a,b,c,d,e,f,g} and let A = {a,c,e,g}...
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...
1. Let U be the universal set with disjoint subsets A and B, where n(U-46, n(A-15, and n(B-14. Find nAn B 2. A merchant surveyed 300 people to determine the way they leaned about an upcoming sale. The survey showed that 180 learned about the sale from the radio, 170 from television, 130 from the newspaper, 120 from radio and television, 70 from radio and newspapers, 80 from television and newspapers, and 60 from all three sources. How many people...
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).
Let A, B, and be subsets of a universal set U and suppose n(U) - 200, n(A) -21, n(B) = 23, (C) -27, [ AB) - 7, n(ANC) - 10, n(BC) - 13, and ( ABN) - 3. Compute: (a) MAN (BUCI (b) AN (BU09
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)
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...
5. Let A, B, C be subsets of a universal set U. Recall for D CU that XD denotes the characteristic function of D. Prove that XAUBUC = XA +XB+XC - XAMB - XAOC · XBNC + XANBNC. Hint: Facts that you may use: (1) Xpe = 1 – Xd. (2) (AU BUC)° = A n Bºn Cº. (3) XEnF = XEXF. (4) XEnFnG XEXFXG. Don't prove these facts.
1. Let S and T be subsets of the universal set
U. Use the Venn diagram on the right and the given data below to
determine the number of elements in each basic region.
n(U)=25
n(S)=13
n(T)=14
n(SUT)=19
Region I contains _____ elements
Region II contains _____ elements
Region III contains _____ elements
Region IV contains _____ elements
______________________________________________________________________________________________________
2. Let R, S, and T be subsets of the universal
set U. Use the Venn diagram on the right and...
Question 1# For universal set U = {a,b,c,...,} (the alphabet) let V be the set of all letters used in the name "Vincent Van Gogh" and let W be the set of letters used in the word "watercolourist". How many members have each of the following sets? Show your enumeration calculation. (a) V (b) VW () VAW (c) VUW (f) P(V) (the power set of V] (d) V W
(a) We want to select three subsets A, B, and C of [n] so that A -C and B C C. How many ways can this be done? (b) We want to select three subsets A, B, and C of [n so that ACC, BC C, and An BメØ. How many ways can this be done?
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