Let A, B, and C be subsets of a universal set U and suppose n(U) = 150, n(A) = 27, n(B) = 29, n(C) = 33, n(A n B) = 5, n(An C) = 9, n(B n C) = 13, and n(A n B n C) = 4. Compute: (a) n[An (BUC)] (b) n[An (BUC)]

Q: Let A, B, C, D be sets. Prove that (a) A × (BN C) = (A × B) N (A × C') (b) (A × B) N (C × D) = (AnC)…

A: Given (a) A×B∩C=A×B∩A×C (b) A×B∩C×D=A∩C×B∩D

Q: . If n(A) = 15, n(B2)= 20, and n(A ∩ B) = 10,find n(A ∪ B)

A: Given: nA=15, nB=20, nA∩B=10

Q: Show that if a < c< b, then fave (a, b) = () fave l(a, c) + C - a | favg [c, b]

A: Solution...

Q: d) Give a recursive definition of the sequence {a„}, n = 1, 2, 3... %3D n if a,= 2 + 1; and a15 e)…

A: d)  Here, given that an=2+1=3 So, for all n, an=3 which is the recursive definition.

Q: Find n(A) for the following set: b) A = { {0}, {1,2}, {3,4,5} }

A: Consider the given set A = {{0}, {1,2}, {3,4,5}}.

Q: Let A, B, and C be subsets of a universal set U and suppose n(U)= 150, n(A) = 22, n(B) = 24, n(C) =…

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Q: Let w be defined as 2 more than the number of digits in the integer w. For example, 15 =4(2 digits…

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Q: 3. Which of the following statements are true? There may be more than one correct answer. A. Ø CA B.…

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Q: A universal​ set, with​ n(U) = 30​, is partitioned into three​ subsets: A,​ B, and C.     If​ n(B) =…

A: we are given n(U) =30​, n(B) =3​⋅n(A), and​ n(C) =2​⋅n(B) also universal set is partitioned into…

Q: Let A, B, C, D be sets. (a) (b) Prove that Ax (B \ C') = (A × B) \ (A × C). Prove that (A x B) n (C…

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Q: A and B be subsets of a universal set U and suppose n(U) = 400, n(A) = 200, n(B) = 160, and n(A N B)…

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Q: Find n(A) for the following set. A= {a, b, c,.., z} n(A) =]

A: Given Data: Set A: {a, b, c,..., z} The set A is consists of English alphabets. English alphabets…

Q: Evaluate the following integral 2.4 21 dx 1²+1 using the composite Simpson's 1/3 rule with 6…

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Q: (19) Prove or disprove ∀ sets A, B, and C: (A – B) − C = (A – C) – (B – C).

A: We will use the Venn diagram show the proof: Left side:

Q: Let a = (5, – 3, 6) and b = (5, 3, 4). (a – 6) × (ã + 6) -| X (a +

A: Given: a→=5,-3,6and b→=5,3,4

Q: A universal set U with 48 elements has been partitioned into three subsets, A, B, and C. If B is 5…

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Q: Find the union of each of the following pairs of sets :(i) X = {1, 3, 5} Y = {1, 2, 3}(ii) A = [ a,…

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Q: Suppose that A, = {-n, -n + 1,..., –1,0,1, ...,n – 1, n} for any natural number n (note that Ao =…

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Q: (1) Let A = {1, 2, 3, 4}, B = {2, 4, 6}, C = {1, 3, 5} and U = {1, 2, 3, 4, 5, 6, 7}. Compute the…

A: By the authoring guidelines of Bartleby, we can answer only first three subparts, please post other…

Q: Let A, B, and C be sets in a universal set U. We are given n(U) = 66, n(A) = 32, n(B) = 33, n(C) =…

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Q: (1.) Let T = {1, 2, 3, 4, 5, 6, 7, 8, 9}.  Suppose five integers are chosen from T. Show that it is…

A: 1) Let us choose a set = {1,2,3,4,5}  In this set, two maximum numbers are 4 and 5. Sum of 4 and 5…

Q: Let A = {1, 2, 3, 4, 5, 6}. Insert the appropriate symbol ∈ or ∉ in the blankspaces:(i) 5. . .A…

A: (i) 5  ∈   A      because 5 is present in  A   (ii) 8 ∉  A       because 8 is not present in  A…

Q: Let A = {1,3} and B = {2,4}. (a) Draw a picture of the set A × B. (b) Compute P(A × B).

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Q: Let n(A) denotes the number of elements in set A. If n(A) =p and n(B) = q, then how many ordered…

A: Given that: n(A)=p, and n(B)=q

Q: Let f(a, b) = (a + b+2) + (2a + 4b + 6)x + (a +b+c)x² and set F = {f(a, b) : a, b € R}. What is the…

A: let  fa,b=a+b+2+2a+4b+6x+a+b+cx2 and set F=fa,b:a,b∈ℝ claim- to find the value of c if f1,0+f0,1∈F

Q: 3. Let A, B, C, and D be sets. (a) Prove that (A × C) n (B × D) = (An B) × (Cn D).

A: Let A, B, C, and D be sets.To prove the equality, we have to show that, LHS is a subset of RHS and…

Q: if n(A U B) = 97 and n(A) = n(B) = 69, find n( A ∩ B)

A: We are asked to find n(A∩B)

Q: Write out the elements of the set 2X where X= = {1,{0}, Ø, {2,3}}.

A:

Q: Find n(A) for the set A. A = {1, 1, 2, 2, ..., 5, 5} O n(A) = 10 O n(A) = 6 O n(A) = 5 O n(A)=3

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