4. Let = {a, b}, A = {a, b, aa, bb, aaa, bbb}, Σ : B = {w € Σ* : length(w) ≥ 2}, and length(w) ≤ 2}. C = {w€ Σ* (a) Determine ANC, A\C, C\A, and A & C. (b) Determine An B, BNC, BUC, and B \ A. (c) Determine Σ* \ B, Σ \ B, and Σ \ C. (d) List all subsets of E. (e) How many sets are there in P(E)?

Q: Compute the component of u along v. u = (3, 2, 1), V = (1,0,1) Consider the following solution…

A: The given vectors are  and .The aim is to find the actual component of along .

Q: 3. It has to: i = (2, –3,4); i = (-5,1,0); w = (4,2,1), perform the following operations: u+v; u-w,…

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Q: n ∈ Z, d ∈ N} and define (a, b) ≡ (c, d) to mean ad = bc 1. For any (n,d) we have (n,d) ≡ (n,d) 2.…

A: Equivalence relation:  Equivalence relations are binary relations that are reflexive, symmetric, and…

Q: 3. Describe span S if: a) S= {(1,1); (2 ,6); (7,12)} b) S= {(1,0,2); (3,2, –7); (–1,–2,11)} c) S=…

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Q: Let U= {x:x E Z,0< x < 10}, A= { x:x EN,x² – 5x = -6}, B={ and C={c, d, e }: a=3 , b=0 , c=3, d=0 ,…

A: (a) Given : U=x:x∈ℤ, 0≤x&lt;10 which means all those integers which are greater than or equal to 0…

Q: Let U = { a, b, c, d, e, f, g} X= {a, c, e, g} , Y = { a, b, c }, and Z = {b, c , d, e, f} α1. Find…

A: Since you have given two different questions therefore we will solve the first for you. IF you want…

Q: Let U = {1,2,3,4,5), A={1,2,5}, B = {1,4,5), and C= {1,2,3}. (a) Find A U (BUC). (b) Find (A U B) U…

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Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: At which of these times (A, B, C, D, E) was runner 1 stopped and runner 2 running? (Select all that…

A: From the graph it can be observed that, At time A the runner 1 had stopped and runner 2 was running,…

Q: Direction: Define subsets of Za, as follows: A = {a | a E Za and a 5} A = {a | a E Za and 3| a} 1.…

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Q: · (b + c) = ² 7. Prove that à. = a · b + ac for all a, b, c € R³.

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Q: 3 1 Let a = 0 |, b -1, and c = |-2|. Justify your answers using proper mathematical notation. 2 5 a)…

A: Given, a=30-1, b=1-12, c=-1-25. a) To check if v=51-4 belong to the span.  This is same as checking…

Q: The percentage of female high school graduates who enrolled in college is given in the table below.…

A: Let x represent time(in years) since 1970, and let y represent the corresponding percentage of…

Q: Let A = ff, I, y }, B = {r, a, t}. Find A x B and B X A. AxB= qafhbuifsfvggbh

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Q: Let U{m,n,o,p.q.r,s,t,u,v} and K{k.l.m.n.v). Find the compliment of K (K').

A: We have to write the elements of U which are not in K

Q: 16. Show whether point N lies on or outside the line AB N=(2,1.5,3), B (0,1,2), A (4,2,4) N=(2,2,5)…

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Q: a. Let U = { a, b, c, d, e, f, g} X= {a, c, e, g} , Y = { a, b, c }, and Z = {b, c , d, e, f} a1.…

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Q: P(3, -2, -1), Q(1, 5, 4), R(2, 0, -6), S(-4, 1, 5) find proj PS. QR

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Q: If u = [5,-3,-1] and = [2,-1,4] find: a) 2-u c) Find G, where F(3,-4,5) and FG = 30 b) |ū+ - 2k|…

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Q: Q2: if A= [{1,2},{3}], H= [{1}, {2,3}], G= [{1,3}, {2}] Show that A, H and G are mutually disjoint

A: Note: " Since you have posted multiple questions. we will solve the first question for you. To get…

Q: Suppose y E span{X₁, X₂}. Explain why span{x₁, x2, y} = span{X₁, X₂}.

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Q: 4. Let A

A: Given,                A=1, 2, a, b, ϕ

Q: 15) Find u x v for u = and v = .

A: Given vectors are, u = -7, 1, 12 = -7 i^ + j^ + 12 k^v = 2, 2, 3 = 2 i^ + 2 j^ + 2 k^

Q: Y D Prox

A: Product of two sets

Q: (3) (i) Determine the number of positive solutions of the equation x1+x2+x3+X4 = 14, where each x;…

A: Thank you for your question!! But according to the guidelines I will be answering one question only.…

Q: 4 The set {# € R : \# + 3| + z > 2} equals Select one O a (-0, -3) U|-,00). O b.(-3, 0). O d none of…

A: If we have x&gt;a then it can be written as: x&lt;-a or x&gt;a Now, we have x∈ℝ: x+3+x&gt;2 Now,…

Q: (m) W ) Given A, Be {sets}, V AC B, A – B= A.

A: Given: A,B∈sets and A⊂B since A⊂B⇒A-B=ϕ we have to prove A-B=A So, these will happen when A=ϕ So,…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 6. A small metal bar, whose initial temperature was 20°C, is…

A: Given,Initial temperature is .Then,Then, by the formula of of Newton's law of heating we…

Q: Let A={2,y,z} and B={3,x,z}. How many distinct elements are in (A×B)∩(B×A)

A: Given, A={2,y,z} B={3,x,z} How many distinct elements are in (A×B)∩(B×A) ?

Q: 26. Let A=61] Find a) A V B. and b) Α Λ Β. B = [id] c) A OB.

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Q: 2. Let A = {a, b, c}, B = {x, y, z}, C = {r, s,t}. Let f : A → B and g : B → C be defined by: f =…

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Q: Determine the, 5 a.) E [3xyi - 10] |=1

A: Sum

Q: Q9. Let keep A = (a, b, c, 1, 2, 3). Let's Insert the appropriate symbol e or ¢ in the blank space.…

A: Concept: The letter Epsilon '∈' is used for the words 'belongs to', 'is an element of', etc.…