Let S(a, b) = {na + mb : n, m ∈ Z}. If s ∈ S(a,b) then sx ∈ S(a,b) for all x ∈ Z How do I prove this?

Q: EXvyP(x, y) is true when there is an x for which P(x, y) is true for every y. A True B False

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Q: Let Q(V2) denote the smallest subfield of C containing Q and V2. Show that Q(V2) = {a + bv2+…

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Q: Suppose X ∼ Binom(n, p). Show that E[X] = np.

A: Suppose Its probability mass function is defined as,Where,

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A: Given I4s=(I4)s We know I4=1 I4s=(1)s

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

Q: Let ū (7, – 4, – 2) and i (6, – 1, 4). - - - Compute the following: v x ú = || и хиE 5(ū x i) = йх…

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Q: Let X={a, b, c, d, e} and let T={X, non zero, {a}, {a, d}, {a, e}, then (X, T) is neither Hausdorff…

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Q: Let n:Z→ 2 the n(Z) =: %3D {3Z,1+3Z,2+3Z} {3Z,1+3Z} {3Z}

A: Let π:Z→Z3Z To find  : πZ

Q: a0 = 1, a1 = 3 and an = an−1 + 6an−2 + 1, for n ≥ 2. Hint: Use the general solution to the…

A: It is given that a0=1,a1=3 and an=an-1+6an-2+1 Let an=A be the particular solution. So an-1=A,an-2=A…

Q: Let A ∈ M (3,R) be invertible and C, D ∈ M (3,2,R) . Solving B from the equality A(B+Ct)t = D, what…

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Q: Let Xis Hilbert Sface and T, SEBO), 2 EF then @+*|| = \|TI|

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Q: Expand а) 1 f(2) = (z – 2)(z+ 1) about z = 2.

A: We have fz=1z-2z+1 Now, using partial fraction decomposition we get for constants A and B:…

Q: What is u × w, assuming that w × u = 〈2, 2, 1〉?

A: Given,w×u=2,2,1 To find:u×w Solution: We know ,by property of cross product of two vectors (say,a…

Q: Assume that

A: Given, X=a, b and  *: X2→X is such that                        x * y * z=z * x * yfor all x, y, z∈X.…

Q: 2) What rule maps ABC onto A'B'C'? A. (x,y) → (x+4, y = 4) B. (x,y) → (x-3, y + 5) 4 (2-0)-²00) AY 5…

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Q: Does S={(1,0,1),(2,1,0),(3,,1,1),(1,1,1)} spans R³ ? Select one: O True O False

A: Given: S={(1,0,1),(2,1,0),(3,1,1),(1,1,1)}

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A: Let gcda,n=1.

Q: Let C = {x ∈ P(A) : ∃y ∈ x, y ∈ A and y /∈ B}. Prove that P(A) − P(B) = C.

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Q: 1-a*** a zi i. La 1-a

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Q: Lot A and B be ovents such that P (A) = 4/5, P (B) = 1/3, P (AIB) = 1/6, where A' is the complement…

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Q: Suppose X₁ and X₂ are i.r.v. and come from gamma(2a, 2). Show that U = X₁ + X₂ comes from gamma(4a,…

A: Given that X1 and X2 are i.r.v. from a gamma distribution.want to show that U=X1+X2 comes from a…

Q: Prove using Rules of Inference: (y € D: P(y)) → (√x € D: Q(x)) P(a) R(c) → ¬(P(a) ^ Q (b)) :. ¬(√z €…

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Q: 2-j 4 5+2j -1 + j F) arrays after execution of each statement: 1) B = A' 2) C-[real(A) imag(A)] 3)…

A: This question is from MATLAB. We'll run the given commands and get the result as solution.

Q: 1. Let A=(a)xn be symmetric and positive definite. Show that a) a>0, i=1,2,...,n. |a|< (aa)², i,…

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Q: (2) Suppose that G, C Zn-r. Then prove that G,-1C Zn-r+1

A: We prove that

Q: Let A, BCR x R defined by A= {{n,m)|n, m € N, 0 < 2m(n + 1) – 3 < 5}, and B = {(1,1), (1,2), (2, 1),…

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Q: Define T: R² → R³ be given by T() = Ar where A = Find an whose image under Tis 18 E -3 -26 -15 1 10…

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Q: Prove if a e G, o(a) =n, then a = reN GCD(n,r)'

A: Given below the detailed solution

Q: Suppose u, v belong to V. Prove that = 0 if and only if ||u|| ≤ ||u+av|| for all a belong to F

A: We have to prove  if and only if

Q: When is S \ T = T \ S for sets S, T?

A: Given that two sets S and T. The definition of S\T=a∈S,a∉T and T\S=b∈T,b∉S. Here, neither of these…

Q: Show that S={(1,0,1), (1,1,0), (1,1,1)} is liearly independent. Give a proof.

A: Vectors in a set are linearly independent if the matrix formed by the vectors as the columns of the…

Q: 15. Suppose that a, b e Z and gcd(a, b) = 1. Prove that ged(a", b") = 1 for m, ne N. N and lot 8 frm…

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Q: S = {x2 − y2 ∈ N : x, y ∈ Z, x2 − y2 > 127}. Prove that S has a smallest element.

A: Given S={x2-y2∈N: x,y∈Z, x2-y2&gt;127} Theorem (Well ordering Principle) Every Nonempty subset of…

Q: Prove (A → A) → A in H. Note: In addition to the axioms and rule of inference of H, you may use any…

A: ↦(⇁A→A)→A 1. Assume (⇁A→A)→A (Assumption) 2. Assume ⇁A→A(Assumption)

Q: Let f(x, y) = In(x²y), where a = s² + t² and y = 2s + 3t. %3D Which of the following is a correct…

A: Given,           f(x,y) = lnx2y3,  where x = s2 + t2 and y = 2s + 3t

Q: Q7: Prove the following: 1) Pr(A) = 1 – Pr(A) 2) Pr(S) = 1 3) Pr(A n B) + Pr(A n B) = Pr(A)

A: Since you have posted multiple sub-parts, we will solve the first three sub-parts for you. To get…