1. Prove the following entailment in SD. P → Q, P → R EP→ (Q ^ R) - -

Q: 土1 OUD Prove that Xor 23 5211で81年 MH Let X,YE L. vis even if and

A: Consider the given information, Let's x and y is belongs to integer. we have to shown that x*y+5 is…

Q: Use Newlon's Me thod with the runclion $r(x)=x^{2}-2$ and inilial value $x_{0}=3: to calculate…

A: Givenf(x)=x2-2            and     x0 =0 newton method  xn+1=xn-f(xn)f'(xn)

Q: Given that en 2= V and en 3=W,express each of the fallowing in terms of vand w a) in zv0/3

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Q: - Show that the norm tion t= aT+B. Use [a, b] onto [0, 1] (7) = 1, ý(7)= T, V т,

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Q: Hor what salue of e dois th. a tollowng matrex haue an Tnverse Q. 2. 2.

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Q: Prove: Given that ll Xllo sl1x|1, <vñ lIXloo for XEL". 2 Show that for

A: The matrix p- norm = operator norm                            ||A||p = Maxx≠0 || Ax||p||x||p…

Q: ) Find the fomily of the equ ation of all lines in 3-space perpen diuler to 2x -y +2u u Given line

A: Family of lines contains parameters.

Q: Find yas a fon chenof x if t. %3D with

A: This is cauchy euler equation and we will solve it by changing the dependent variable

Q: A liner tragfematin defimeed by a malrıx let IRR be a lineor tras ler malin. defneed by Tv) - Av ;…

A: I have proved Linear transformation using the definition

Q: Functional theory and functional analysis

A: According to the given information it is required to prove that:

Q: Show that (hcs) de = 1 In 27 e %3D 2. 20 (ite")(2 + 1)

A: To show: ∫0ln 2e2x1+ex2ex+1dx=12ln2720. Concept used: Integration of ∫1vdv is equal to ln v+C.…

Q: Prove that %3D 3 and hence. deduce that. 3--(n+3)Jn43+ (n+s)Jnes to 2.

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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: find the fimet Qurtal dernratives 7 respect to rarraes X,4,Z.

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Q: 2. Let X, Y c R. Prove that X U (Y – X) = Y if it is true. If not, give counterexamples to explain.

A: Given statement is false.

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: y Verify Euler's theorem for u = x' In

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Q: Find the ared of the reyion R bound ed.by and the liney=x+2 2. 2. =y-yand the line y--x ......

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Q: dy If then de impossible to calculate O In(æ)

A: 7.  slope of tangent line  slope at point ( 4 ,2 )

Q: et X~U([-, 1) and let y = tan(r), show that y Cauchy(0, 1)

A: # using Jacobian transformation we have proved that y=tanx follow Cauchy distribution (0, 1)

Q: Find the of im < Re z< £ un der w-

A: Substitute w=u+iv and z=x+iy in the transformation. w=1zu+iv=1x+iyu+iv=x-iyx+iy.1x-iyu+iv=x-iyx2+y2…

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: Fin d the sc cond soluhen prr tk edo te edo If Konow that y, =x IS a solotień

A: We will reduce the order of the given given second order homogeneous differential equation using the…

Q: 1f itwas x25ect, yatunt prove Thut dy

A: Simple derivative

Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.

Q: In Let x, y ER" be given. (a) If ||x|| = ||y|| = 1 and x - y = 1, show that x = y. (b) If ||x|| ≤ 1…

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Q: Show that Z, dv=2010 %3D if B= 2) : -1 Śn s3, ISySY,e

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Q: Show for Re(z) > 1 ex – 1 dr = T(z)5(2). et – 1

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Q: # if Alu) is a differentimble veetoru u and l A(W) Il = 1 . fonetion of Prove that dA is…

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Q: ) Prove that sac"()/T sec

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Q: Let -{[:);}--{:)[:} -{{)}} Both B and C are bases for R2. If {x}s =: -[:], what is {x}c?

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Q: (3) In R² with the standard topology: {(x, y) | x² + y² {(x, y) | x² + y? > 1}. = 1}, {(x, y) | x² +…

A: In a topological space R2with standard topology. A  subset O is open if at each point x in O there…

Q: 12 २ (४) = dt | २स Prove !- \) ২-০০) = २(-०० ) 3D \

A: Given that Qx=12π∫x∞e-t22dtTo prove:1. Q-∞=12. Q-x=1-QxSolution:we know that ∫-∞∞e-x2dx=π       ...…

Q: Give en exem ple of e: neer trensforme tion thet is not invertibl. V-> v onto but

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Q: 3. If u= (x+y +z') , prove that +y

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Q: Ju 20²u c² of2 (r, t) = u(x,0) = 0, ut(x,0) = 0 u(0,t) = 0 u(1,t) = 0. da2(x, t) + XX , 00,

A: Introduction: The basic method to solve a partial differential equation is the method of separation…

Q: Suppose u, VE Vand ||u|| < 1 and ||v|| < 1 . Prove it: V1- ||u||?/1- ||u||2 <1- (u, v)|

A: Suppose u, v∈V and u≤1 and v≤1 We have to prove that 1-u21-v2≤1-u,v Here, we have  u≤1 and v≤1 Also,…

Q: Prove that (A = B) where (A = ax + ay + az) and (B = bx + by + bz)?

A: Given- A=ax+ay+az and B=bx+by+bz To Prove- That A=B

Q: O Evaluate: | (In a + xe" + Vry) dy

A: Solution of the problem as follows

Q: and are 2 soihions and w Cy,,Y2)(to)to what con conclude ? we

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Q: Show that U. AS cuhere N= {3 unaluralnun %3D

A: To proveG={N,*} is not a group under binary operation a*b=ab where a,b∈N

Q: Prove the following: %3D

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Q: Assume that a1, a2, ..., an E R (with n > 2) such that a1+a2++an = 1. Prove that af+az++a > 1 (Use…

A: Cauchy-Swartz Lemma : For any real numbers  and  the following inequality holds  ,

Q: 2! ODEV de venten egrimin yözyım alonını bulumz eksni etrafioda döndənuess te duçon

A: A=integration a to b y(t) x'(t) dt

Q: pes of animals are treated by at least on r. Scott, and Dr. Baker)?

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Q: Let fun chan defined by g(2) = V Z+8' –-8, ts devivalie z+h+8- Vz+ 8 is equal to the expressian. A)…

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Q: s defined over ai at one point in tl асcordi

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Q: Show that Z/mnZ is isomphoric to (Z/mZ)×(Z/nZ) where gcd(m,n) = 1

A: Concept Used:( The First Isomorphism Theorem) If ϕ be the  ring homomorphism from G to G then…

Q: If e-ispure imaginary W hat Restriction is placed on z?

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