Let a and y be real numbers. Prove hat, Say>I1, hen>2 ory>L

Q: then -u is a unit in R.

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Q: If A= then A" + nl is equal to

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Q: Let p e Z+. Does there exists a positive multiple of p that contains only the digits 7 and 0?…

A: we have  to find a positive  multiple  of p that contains  only  7 and  0 for some p in Z^+.

Q: Let A = {x ∈ Z | 6 divides x} and B = {x ∈ Z | 3 divides x}. Prove that A ⊆ B, and then prove that…

A: We can prove using like showing every element in one set is an element of another set like that.

Q: Use proof by contradiction to prove that if x + y > 2, then x > 1or y > 1 (or both).

A: The method of contradiction is used to prove a statement or a set of statements. The inverse of the…

Q: S. Use the theorems and given information to show that r

A: The figure is as shown below : Given, ∠4 = (13x-4)o, ∠8 = (9x+16)o and x=5

Q: Given and prove

A: Given,

Q: Let X ∼ Bin(n, p), and let Y = n − X. Show that Y ∼ Bin(n, 1 − p).

A: Here X follows Binomial with parameters n and p. Here, Y=n-X. Then Y takes the values n-0, n-1,…

Q: b, c e R such that abc

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Q: K is the midpolnt of GI and HI | GJ. Complete the proof that AHIK E AJGK.

A: Given,            K is the midpoint of GI¯ and HI¯ ∥ GJ¯

Q: Let A 3 and U = |- Then A2017U is equal to

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Q: Let A, Be M, (C) be positive definite. Prove that (4+ B)" s(A" +B").

A: Let A,B∈Mnℂ be positibve definite.  To prove A+B-1≤14A-1+B-1 Since, A and B are positive definite,…

Q: Prove: If a > b > 0, then 0 < 1/a < 1/b.

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Q: Use the given information to prove that ADEF ADGF.

A: We need to find out the reason and complete the proof .

Q: Show that if x ~ Nm (u, 2), where N is positive definite, then (x – u)'N-I (x – µ) ~ Xm: 2

A: Given  x~Nmμ,Ω, where Ω is positive definite.

Q: Prove that for Vr > 0, s > 0, √√r + √√5 ± √√r + s r, s

A: # As per the guidelines we are entitled to solve one question at a time please resubmit the other…

Q: Q) Let Tright on R ? {(a, o0) : a € R}U {¢, R} . Prove that Tright is toplogy

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Q: Let a and b be any real numbers. Prove that Cov (ax, by) = abCov (x, y).

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Q: メ人 xp- Vtan (e) sec?(e) de Evewale Jhe Jollowing! op (e)as (a)

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Q: If Do, D1,..., Dn... nEN, are dense open sets of reals, then the intersection D = 0 Dn is dense in…

A: Condition: Dn is the open dense sets of reals, for all n∈ℕ. To find: Intersection of infinite open…

Q: If A' = g;a,rsys , Yi = birx, , and a;,b,j = dij. Find A' in terms of the x,

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Q: Let a, b ∈ R with b ≠ 0. Show that R(a + bi) = C.

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Q: lar, let m = 2 and n e of A and B such that

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Q: (a) Prove that de 2n a>b>0 Jo a+ bcose Ja? - b2

A: We will use basic knowledge of Integral Calculus and trigonometric identities to solve this…

Q: Show that if a, = (a" – B"), where a = (1 + v5)/2 and ß = (1 – V5)/2 , then th An = an-1 + an-2 and…

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Q: prove the following : a) a0=0 b) (-a)v=a(-v)=-av c) av=0 implies either a=0 or v=0

A: What is Identity and Inverse Element: Identity element is that element which on performing binary…

Q: . Given: LAOM and LMOC are supplementary. Prove: x = 50

A: To prove that x=50

Q: Use algebra to prove | (ka, kb)| = |k| • | (a, b)|.

A: To prove: |(ka , kb)| = |k|.|(a , b)| L.H.S  = (ka , kb)            = k(a, b)                  . .…

Q: Show that if A is singular, then adj A is also singular.

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Q: Q Let 8=R and Prove disprove that zis atopdagy or on R.

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Q: (a, b) is measurable. ulgn O ihi O

A: I will use the definition of measurable set.

Q: 30 Let A, B E M, and suppose that A² = 0 = B². Show that A and B are unitarily similar if and only…

A: I

Q: Prove: If a < 0 and b > 0, then | a  + b | < | a | + | b |

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Q: Hi I have attached the question. Thanks

A: To prove that the complex number z is real under the given conditions

Q: Let a1,..., an be real numbers. Show that ajan + aja2+ aza3 +... + an-1ªn < i=1

A: We are given that a1, a2, ... , an be real numbers. We need to show the following statement.…

Q: Derive the UMVUE of h(0) = 0* where k = 1,2,...,n is a known integer. Hint: Use the interpretation…

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Q: Let, aj = 3 and for n > 2, an = 2an-1 +1, express a, in terms of n.

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Let A = and U = Then A2017U is equal to ... B

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Q: Let X = R, and M = {0}, then span (M) = %3D %3D OR O {0}

A: If, M = {0} then, span(M) = {0}

Q: Prove: Let a, b, c, d be real numbers. If a &lt; b and c &lt; d, then a + c &lt; b + d.

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Q: 2. if f(x)=D x+2 and gu) = x+3. gla)= of メ+) gof and determine if it is one ind and onto [3,00) ??…

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Q: Which postulate justifies that ДНАМ~ДСОW? a. AAA С. ASA b. SSA d. SAS

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Q: . Prove with the usual notations that: (b) A +V =- (c) A= SEŽ (a) EV = VE = A

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: tet r and m be integer, prove that 17/20+3m iff, 17/9n

A: Solution

Q: Suppose AnB CC\D and x E A. Prove that if x eD then x ¢ B. (Hint: prove via contrapositive)

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Q: (a) For integers a, b, q, r, prove that if a = bq + r then (a, b) = (b, r).

A: Since you have posted a multiple question according to guildlines I will solve first(a)    question…

Q: Suppose that fo sf,:X-gy and g,-3 YoZ Prove that (Hint : First use ce) to show that gfe g,, and then…

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Q: Let A + 0 and ACB. Show that NB CNA.

A: Given :A≠∅A ⊆ B