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A: The set of vectors v1,v2,…,vn of a vector space V are said to be an orthonormal set of vectors if…

Q: Let! aset os R, sho that whe ther Tbe acofinite to pology on (R,T) is To-spuce and TisPuceand or not…

A: The given question is related with topology. Given that Τ is the co-finite topology on R . We have…

Q: Let E = Q(V3, i). Then, Gal(E/Q) is cyclic. %3D False True O O

A: Given  E= Q(3^1/2,i) Gal(E/Q)  is cyclic .

Q: Let C: z-3 and I – 6dz. ONone of these

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Q: Complete the proof that ZSTV LTSV. T R Statement Reason RU I ST Given ZRUV LR Given ZR ZSTV 4. ZTSV…

A: We know that, Alternate interior angles are angles formed when two parallel or non-parallel lines…

Q: Suppose is dhe iavene faction of a diffarentiable šunc- tica fand let Glu) -1/r . E3) - 2 and /3) -…

A: G(x)=1f-1(x)f(3)=2 , f'(3)=1/9

Q: Let E={(r,0,z) : os es T, OS zs 1, 5Vzs rs 5. Compute

A: Introduction: The triple integral ∫∫∫Ef(x,y,z)dV with the region E=(x,y,z):a≤x≤b, c≤y≤d, e≤z≤f can…

Q: Consider the following. u 3 (-4, =(-4, 6), v = (1, 1) (a) Calculate projy u.

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: メ (myst メート→ Q(2,4) where: Path C くz rom ○)と to over the Evaluate the

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Q: let X=R and R={Caro): a ER 3U {8IR3 C Right way totolyy) c heck Ris

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Q: Jin Let G beagreupsuch that I6tefs thens

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Q: Suppose ū = (–5, −4, −5) and v = (–2, 4, −5). Then u x vis Uxuis and

A: Topic- Cross Product of Vectors

Q: Suppose that (Q x Q, +,.) is a ficld where (x, y) + (z,w) (x+z,y + w) and (x, y). (z, w) (xz +2yw,…

A: I have find identity of the field and then inverse

Q: d set): Let (M ,d) be a (SUT)' = S' U T'.

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Q: 11. Let SC R and suppose that s := sup S belongs to S. If u ¢ S, show that sup(SU {u}) = supfs*, 4).

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Q: Let A,BE Mmna Shaw that vTAw= V' Bw for all VER™ end WEIR" if and only if LA=B. %3D

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Q: #20. if A is a Ux4 matrx such that tHhe cauathon anly the trwiat soluhan , then the ranme Ax=0 has…

A: Given :  A 4 × 4 matrix such that AX = 0  Has only the trivial solution. Then

Q: Let D be digraph. If id(x) > 0 for all x ∈ V (D), then D contains a circuit.

A: Given:- Let D be digraph. If id(x) > 0 for all x ∈ V (D)

Q: 6. If u=,%) prove that xu, + yu, + zu, = 0

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Q: 5. Let H= [ (û ¿)I a,b,c EIRI, show that: (H,+) is a sub gromp of (M,+).

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Q: 2 Caleudale the verbor fanetiom dwsugene and Cuele g the fallowang

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Q: 4 Let X,) be a pankizlly oadered e For x,y € X deftre xLy eff x sy and x#y. Pucose the Fallowiag:…

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Q: 9. Let u AB and v = =PQ where A=(-4, 6), B = (3, 3), P = (4, 5) and Q = (-3, 8). Can you verify that…

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

Q: A ber coatais 6 whine, 4 bMar and 5 red balk. 4 balh ar chea at randem Let X denote the ofblae bub…

A: We have to find given probability.

Q: =8, d=9 ation u such that (a, b, c, d) = p

A: The value of a, b, c and d are given as follows, a=5, b=13,c=8,d=9. To find the permutation μ, such…

Q: Consider o Con Assume He holding holding Vo =Vi =d, thatis, to the ofter going 1. Draw the Pre

A: Hi, there! As per the norms, we are allowed to solve single question at a time when multiple…

Q: Let Xionne Xn be aris H c'cid) From PlO), or QcOi Findthe MP test g sige a to test Ho:G-Be N5 H,:…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: let A, B and C three are OVerlapping Sds anly using Venn that (B-u(e A) diagrom Show A-B

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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: 20. Let -(). -- (). (). u = w = If au + yv = w. (x, y E R), then a - y = (A) 2/3 (В) —3/2 (C) 3/2…

A: To find  The value of x-y

Q: 7) Assume dim V = n, dim U = k, dim W = n - k, and U + W = V. Prove that Un W = {0} and V = U OW.

A: Given, dim V=n, dim U=k. dim W=n-k, and U+W=V.To prove that  U∩W=0 and  V=U⊕W.

Q: #3. Let n be an mteg er with nz1 and Let b., bzba be ... positive real nmmbers, not all egual, such…

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Q: Showw Fom yex)=D90Y,(x) + a, y,(x) that seris sol utron is of the hene y,cx) contains only even…

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Q: Let S be a 50-element subset of {1, 2, 3,...,87} and let T = {s+11 :sE S}. Prove that SnT+ Ø.

A: This is a question of Set theory, application of the Pigeon Hole Principle.

Q: Find propositions P(x, y) and Q(x, y) that demonstrate tha (Vxay, P(x, y)) A ay, Q(x,y)) is…

A: Let Statement 1: ∀x∃y, Px,y∧∀x∃y, Qx,yStatement 2: ∀x∃y, Px,y∧Qx,y

Q: let t={usx8 x-uiscoantableiuioi then Tis called Tcof

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Q: Prove that du Inlul + C where n= -1 u

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Q: Let A1, A2, ... , An be any n sets, n 2 1. Show that (U-1 Ar) = U=1 Ar %3D

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Q: جليلة Let I = [= 1,₂1] ISR interval w that I is negligible Set.

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Q: Let A=(aij)nxn be symmetric and positive definite. Show that laul< (anan), , lis = 1,2,..n 9

A: Given: Let us consider the given, A=aijn×n Let's prove that aij&lt;aiiajj12,i,j=1,2,...,n.

Q: Let X, , X>, . X, be a vandam of size I For o hormol distribuien with unrur M and $6. IS 5 Xi = 132…

A: Provided information is ;  sample size(n) = 11 ∑i=1nxi  = 132 ∑i=1n(xi-x¯)2 =99 confidence interval…

Q: show that whe ther RERiemman L-,1} yot

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Q: Let X + 0, |X|> 2. Then (X, Tna) is not To -space. Select one: True O False

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Q: 5. Prove the following entailment in SD. A M, M (Q A K), A K VL

A: Given:                         A→M, M→Q∧K, A ⊢ K∨L To do: Prove the given entailment in SD.

Q: Suppose that a,beG such that a = m and b =n with Gcd (m,n) = 1. Then n | is in mn

A: Suppose that a, b∈G such that a=mb=n and Gcdm, n=1 i.e., m and n are relatively prime. We will find…

Q: ® Complete the proof 4 the friet deitaihuteje 10 lav cin In, liky To do this (3 real nembeo), a.…

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Q: 『/ f メ,メ K、 be ars fo U()e) Tet Yu be the Larsest s the n bservotien an unbiesed estometor fr 6? E-…

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Q: Is f(x, y, z) = 8 In x+7 In y+5 In z homothetic? Of(x, y, z) is not homothetic Of(x, y, z) is…

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Q: Prove that if A C R and t > 0, then |A| = |AN(-t,t)|+|AN (R\(-t,t))|-

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Q: If A = {1,2,5,8, 9} and R = {(x, y) E A X A 3 x + 1 = y}, S = {(x, y) E A X A 3 y +1 = x} %3D %3D…

A: SOLUTION-

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.