Is A – (B U C)= (A – B) N (A – C)? Prove it or disprove it.

Q: Prove the following fact: A" = 3"-1A. 1 1 1 1 1 1 1 1 1 A =

A: Given, A =111111111  We have to  prove An = 3n-1A

Q: - 21 , Prove that + (n? m' ) yn=o 2.

A: According to the Leibnitz theorem, dndxn(uv)=C0nunv0+C1nun-1v1+C2nun-2v2+... Formulae used:…

Q: 4. In the figure, if AB = AC and BO = OC. Prove that ZB = C .C B

A: a). Given: AB=AC and BO=OC Prove: ∠B=∠C

Q: 6. let A 6 6 -3 -2 -1 -2 -5 -3 diagomol moatie over te Lield R? Oer C I Is A similar do a

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Q: What is eh REF of B? 1 2 1 1 B = نه who 1 0 -1 به T NC vсы N 5 0 2]

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Q: 5n² is O(n³)

A: Suppose fn and gn are positive functions. We say that fn∈Ogn if there exist positive constants c, n0…

Q: Q.2. Proof that V= u8--

A:

Q: 12. What can you conclude from (PV Q) ^ ¬P? Prove it.

A:

Q: v.(AX 8) - 8 ·/TXA) – A (vX 8) Prove the earuation.

A:

Q: What is the first step to prove that S, 2+4 + 6+...+ 2n = n(2 + 1)? n(n + 1)? O Verify that S, is…

A: Here we have to determine the first step to prove that,  Sn⇒2+4+6+..........+2n=n(n+1)

Q: Given: 23 = Z1 Prove: АВ АС 2 3/6 E

A: Given: The angle ∠3 is equal to ∠1. Concept used: If the two angle of a triangle is equal then side…

Q: ndersta

A: The condition for weakly stationary processes is that the mean and the variance are time invariant…

Q: Prove for all mEw and n E w, we have that m+ ·n=m・n+n.

A: Given that m,n∈ω. To prove: m+· n=m·n+n

Q: 11. What theorem is used to prove that BD 1 AC? C В. D A

A:

Q: Let (W, t > 0) be standard BM. Show that P(n|w,1 – Wa sc) → as n → 0.

A: From the given information,  (Wt, t≥0) be standard Brownian Motion. Note: In the given situation,…

Q: Q3: Prove that (9":n e Z) (3":ne Z) but (9":n E Z) (3":n E Z).

A: We have to prove that 9n:n∈ℤ⊆3n:n∈ℤ but 9n:n∈ℤ≠3n:n∈ℤ

Q: Prove that Ek=0 C) 7n-k . 2k = 32n %3D

A:

Q: Suppose m e Z. Prove by both contrapositive and contradiction that if m² + 2m + 4 is odd, then m is…

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Q: Find simpler expressions for the quantities in Exercises 45–48.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Q3: Prove that (9":n e Z} S {3":n Ee Z} but {9":n e Z} (3":n E Z}.

A: To prove:  {9n:n∈ℤ} ⊆{3n:n∈ℤ} but {9n:n∈ℤ} ≠{3n:n∈ℤ}

Q: Example 12. In a, b, c are in A.P., prove that the following are also in A.P. () ь + с, с + а, а +…

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Q: Prove that E, k2* = (n – 1)2"+1 +2 for all n > 1. =D1

A:

Q: Prove NIn, +oo[= 0 ! n=1

A: To prove that ∩n=1∞[n,∞)=∅. Suppose that x∈∩n=1∞[n,∞). Then, x∈[1,∞), x∈[2,∞),.... That is, x≥n,…

Q: locally Lipschitz in (t,x)E[a, b]x D.

A:

Q: Prove that Z(Sn) = {e} for n ≥ 3.

A:

Q: 27) Calculate AC, BC and (A + B)C. Also, verify that (A + B)C = AC + BC 0 6 71 ΓΟ 1 1] 2 If A = -6 0…

A:

Q: 11. Given: AB CD, EB FD AB TCD Prove: a. AAEG ACFG b. AG GC

A: Given:

Q: Show that for all n e Z, n? – 3n +17 2. -

A: Given: For all n∈ℤ, n2-3n+1≠2

Q: 1D Klove mothe mohical Inoucton 1. Mothe motical Imohchon forallinteges 2-3 nln+1) nt)

A: let this a statement P(n) For P(1) THE BOTH SIDES OF THE STATEMENT WILL BE 11+1=11+1  so P(1) is…

Q: %3D 107° 73 (9x + 46)* O 2021 McGraw-Hill Education

A: We know vertical opposite angle are same value.

Q: o In general a;jk(Xi + Yj)Zk = a¡jkX¡Zk + AijkYiZK - True - False

A: We have to prove or disprove that

Q: Prove, using an element-chasing argument, that {15n : n E Z} = {3n : n E Z}N{5n : n E Z}.

A:

Q: Prove indirectly: "V n E Z, 4 ł (n² – 2)."|

A: Ans:Let us assume that 4/n2-2;∀n∈zthen we have there exist a positive integer k such…

Q: O N (AT) = R(A)-

A:

Q: Let a = 8 and b = 9. Find m,n E Z such that am+bn =1.

A:

Q: 9. Prove or disprove. (a) Vn e Z*, n² < 2". (b) Vm e Z, if m is odd, then m² is odd.

A: In this question we have prove if this equation are valid or not.

Q: Suppose b1 + *+ bm < n. Prove that b,!bm!< n!.

A:

Q: 10.B.4: Suppose TE£(V) andcEF. Prove that det (cT) = cdim V det T.

A: Here given that T∈L(V),is the set of linear maps from V to V.

Q: Consider z1 = 1 - j2 and z2 = -2 + j3. Determine Im (21)?

A:

Q: 53. Suppose that a + 0. (a) If a · b = a·c, does it follow that b (b) If a X b = a X c, does it…

A: Given a, b, c are three vectors and a ≠ 0.

Q: es lls ew zeiflucifiib ons einiseen stigesber Show that for neN, (2n)! ' (r!)² ((n −r)!)² - 7=0 2n -…

A: We will use binomial expansion to prove given relation

Q: 6. Prove that, if a, b e Z, then 3a? – 4b – 5 0. - -

A: Answer

Q: Show that |Re(z)|+|Im(z)| < v2|z| for any z e C.

A: The solution is given as

Q: (a) Ha: B1 0, with n = 26 andt=1.91 <p< 1 (b) Ha: B1 # 0, with n = 12, b1 = 0.16, and sp1 = 0.06 %3D…

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Q: If det A= 0 why is det A+ = O? If A has rank r, why does A+ have rank r?

A: Given Data det A=0   Suppose the column and row of the matrix are linearly independent. The matrix…

Q: Under what conditions on A and B is (AB)-1 = A-1B-1? Prove your assertion

A: Assertion: If A and B are commutative, then  AB-1= A-1B-1.

Q: I find B such that AB = C. If 5 0 3 A = 2 01 9. C = 3 5 c- (* :)

A:

Q: a) How has he arrived at this conclusion? b) What assumption is he making? c) Do you agree with his…

A: Given, P( Harvard accepted)=0.053 P(Dartmouth accepted)=0.1 P(Penn accepted)= 0.099 P(atleast one…