Problem 2: We have three sets A, B, C with the following properties: (a) |B| = 2|A|, |C| = 3|A|, (b) |An B| = 16, |AnC| = 17, |BC| = 20, (c) |AnBnC| = 3, (d) |AU BUC| = 130. Use the inclusion-exclusion principle to determine the number of elements in A. Show your work.

Q: Given A,B and C required to prove that A\(B\C)=(A\B)U(A∩B∩C)

A: Given  A, B, C are any three sets  We have to prove  A\(B\C)=(A\B)U(A∩B∩C)    Let X be unversal set…

Q: 3. Use the definition of a convex set to show that if S₁ and S₂ are convex sets in R+", then so is…

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Q: 3. In each case suppose R" has the norm ||l inclusions: = max {ril,., r.}. Prove each of the set (a)…

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Q: Consider a choice problem with set X=(x, y, z), and consider the following choice structures: (B,C),…

A: WARP: A choice structure (B,C(·)) satisfies the weak axiom if for some B∈B with x,y∈B we have…

Q: 6. Show that the sets S = (1,5) and T = (0, 00) are equinumerous by finding a bijection from S to T.…

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Q: Prove, for all sets X and Y, “the inclusion-exclusion principle”, i.e. #(XUY)+#(XnY) = #(X)+#(Y),…

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Q: write each of the following sets by listing their elements between braces. Please show work.

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Q: 9. Using the notation of the previous problem, prove that for sets A, B, C, DE P(X) AAB = CAD → AAC…

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Q: 4) Define on the cartesian product of sets R:=R x R = {(^, z) | A, z E R } an addition and a…

A: We first show that R is a commutative ring. That is we show that R is commutative group under…

Q: 4. Find the number of integer solutions for the following equality using inclusion-exclusion method:…

A: We shall use counting using coefficients

Q: Problem 6.3. Show that for any sets A, B, C the following equalities hold: (1) A × (BUC) = (A × B) U…

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Q: For: A=1; B = 8; C=3; D = 1; E = 3; F = 0. Answer: Consider in M,v, (R) the subsets U and W, where U…

A: The given values: A=1; B=8; C=3; D=1; E=3; F=0 The Subset U is defined by, Substitute C and D value…

Q: Is L = {x+ix : x ∈ R} an open subset of C? A closed subset of C? Both? Neither? Justify your answer.…

A: To analyze : The subset L=x+ix : x∈ℝ ⊂ ℂ

Q: Let A,B,C⊆U. If n(U)=65, n(A)=24, n(B)=28, n(C)=32, n(A∩B)=15, n(A∩C)=7, n(B∩C)=11, and…

A: Given information: nA'∩B'∩C'=9nU-nA∩B∩C=965-nA∩B∩C=9       nA∩B∩C=65-9…

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Q: The dimension of the set W = {(2t – s, s, t) : s, t e R} of R is equal to: %3D

A: The dimension of the set W={(2t-s,s,t) : s,t ∈ R} of R3 x=2t-s y=s z=t (t,s) ∈ R   This can be…

Q: Consider A = (x, y,z) and B = (w,x, y). If U = A U B, which set is equal to (B\A)'? Note: B\A = B-…

A: The union of set A and B is denoted by A∪B has elements both inset A and B The complement of A has…

Q: Exercise 2.29. Pick several different subsets of R, and for each one, find its interior and boundary…

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Q: Recall sA : R" → R is a support function given by SA(x) = sup p•x PEA %3D Let A, B be nonempty…

A: The given function sA:ℝn→ℝ is a support function defined as: sAx=sup⏟p∈Ap.x (a). Let A,B be non…

Q: 6. Show that (an)neN C R is bounded if and only if lim supn→∞ an < +∞o.

A: To Prove:  ann is bounded sequence if and only if limsupan&lt;+∞.

Q: Describe the following sets by roster method: Example (i) {x : x + 5x + 6 = 0, x e N} (iii) {x : 4x…

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Q: The number of non-empty subsets of B is |{S:SC A, S = 3 and Sn B = 0}| = max {|S|: SC AUB, SNA| is…

A: Given that A and B are finite sets satisfying A=6, B=7, A∩B=2. Since, B=7. So, total number of…

Q: 1. Let D= [-2,3) U {-3, T}. Determine the following: (a) max D, (b) inf D, (c) interior ED (a) b

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Q: Let V = {(a1, a2): a₁, a2 € R}. Define addition of elements of V coor- dinatewise, and for (a₁, 02)…

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Q: Assume that AA and BB are disjoint subsets of UU, and that n(U)=55n(U)=55, n(A)=23n(A)=23, and…

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Q: 1. Let X={a,b,c} and Y={1,2} then X×Y ={(a,1),(a,2).(b,1).(b,2),(c,1).(c,2)} - Consider U =…

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Q: a) n(A) =    b) n(A∩B) =  c) n( B' ∩ C' ) =

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Q: (1) Let X={a, b, c}, Let r-{0, X, {a}, {b}, {b, c}}. Which of the following is an open cover of X:…

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Q: 6. (a) Let A, B, be subsets of R. State the conditions which make the pair (A, B) Dedekind cut. (b)…

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Q: Show that if C and C'are two linear codes equivalent, then the duals Cand C are equivalent.

A: Here we have given that C and C' are two linear codes equivalent. We need to show that the duals C'⊥…

Q: .    Verify that: a)    (A - B) – C = A - (B ∪ C) b)    (A Δ B) ∩ B = B - A

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Q: a) Define AAB = (A − B) U (B − A), where A, B are any two sets. Show that (ΑΔΒ)ΔC = ΑΔ(ΒΔC).

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Q: 1. Prove that for all sets A and B and n € Z, n ≥ 1, the following holds: n (a) U(A₁\B): i=1 = n C…

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Q: Q: Let z = -4 V3 – 4 i %3D A/ Find the following : 1) Iz| 2) arg (z)

A: Since you have posted multiple questions but according guidelines, we will solve first question for…

Q: QI: Find Sup; Inf; Max; Min for the following sets: (a) S = 2 : m,n EZ+; (b) T = {nez}. n+1

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Q: 4. Determine which of the following subsets of R2 are open, closed or none of them. (a) {(x, y) =…

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Q: This question concerns the following subsets of R²: A = {(x, y) = R² : (x + 1)² + y² ≤ 4}, B = {(x,…

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Q: Determine whether the following sets are convex (1) {(x,y)=√x + √√]]l}

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