Premises: p → (q ^r), s → r, r → p. Prove: s→ q.

Q: prove thats. u.w V.W V.

A:

Q: a. Show that Ø, R E T. (by definition of Topology)

A:

Q: Prove that (C, +) ≈ (R × R, +).

A:

Q: Prove that c(u × v) = cu × v = u × cv.

A:

Q: 18, then Ku = 3 and µ4 Af U2 %3D %3D Select one: O Platy O symmetric O Lepto O Meso

A: Solution-: Given: We find

Q: Show that : sup {reQ:r<a} =a, for each a e R. %3D

A:

Q: Let feC-2,2], fo-o. Prove that Max -2

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Q: Prove using the IVT,  √2 exists.

A: To prove using IVT, 2 exists.

Q: Let Z, = 2 cis 30° = 3elli %3D Z = In (1 + i) %3D If Z = Z,Z, + Z, Find Z].

A: From the given information. Write the complex numbers Z1, Z2 and Z3.

Q: Verify f U= n1 V = 234 43 snyz %3D +23- 422-24-42- dependend %3D fundlarelly are

A: We know the identity: x3+y3+z3-3xyz=(x+y+z)(x2+y2+z2-xy-yz-zx) --(1) We are…

Q: Functional theory and functional analysis

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

Q: 2)Evaluate exdA ,Ris bounded by y = x² ,y = 1

A: By using Fubini's theorem we solve the given problem.

Q: 8.F. Ifx= (1, I, --- ,)€R", define x, by e that z- l, is a norm on R'. Prove

A: Given that x=x1,x2,..,xn and x1=x1+x2+...+xn. The objective is to find the whether x1=x1+x2+...+xn…

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: 16. Write a two column proof. Given: OSTUV U V. Prove: AVXS = AUXT T S 8.

A:

Q: Which condition would prove AJKL ~ AXYZ?

A: Here we have to find the ratio between two sides such that the given 2 triangles will become…

Q: 8. Show that, for u, v E R³, ||u|| ||| = (u - v)² + ||u x v||².

A:

Q: Q: Prove that tim %3D

A: We have to prove the limit

Q: 27. Prove in detail that Q(/3+ 7) = Q(/3, v7).

A: We have to prove given equation.

Q: どタ -e -at u Ct) = (a +jwjñ+!

A: To prove that tne-atut↔n!a+jwn+1 It is known that  ut=1 , t&gt;0=0, t&lt;0 Therefore,…

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: If divF (x, y, z) = 0 for all (x, y, z), then curlF (x, y, z) = (0,0,0) for all (x, y, z).

A:

Q: Prove that if r>3 and y > 4, then ry > 11.

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Q: Prove that Vtan a de – 7//2.

A:

Q: let X be 4-VV flon)= To Finel ECX) oedECXY)

A: f(x) = x/10 where xx = 1,2,3,4

Q: Prove that • I %3D

A:

Q: Q: Prove that tim x"- a" %3D

A: we have to find the limit of the expression

Q: az Q.7 If z(x + y) = x2 + y?, show that lax = 4 ду. - +(1 - ax ду.

A:

Q: 4. Prove that, VR, -11-

A:

Q: Let f(z, y, z) = z2 +y? + z²,z = /utv, y = /u – v, and z= uv, Find in terms of u and v.

A: we have to partial derivative with respect to u by using chain rule

Q: Prove that. 2/nJn-(n+2)Jne2 + (n+yjJney --- 3. end hence deduce that. 1xJn - (nti)Jnas -…

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Q: Let f lany) prove that' flany) di f feren tiable I5 not point lo,0) .

A: Let the function be fx,y=xy Note:  [ We can say that f is differentiable at (a,b) if f is…

Q: Prove that Z(D,) # {1} if and only if 2|n (hint: if 2|n look at ri).

A: Let us suppose, Dn=e,r,r2,..,n-1,f,rf,..,rn-1f and nis divided  by 2. Then, n2 is a integer. We see…

Q: 3. Prove that: na” u[n] = az (a-z)2

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Q: 12. Prove: ΔUΧΖ-Δ AUXZ AYVZ ~ Z.

A: Given: chord UXChord YVand the Center ZTo…

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

A:

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: 2. Show using only the Cauchy-Schwarz inequality that if u,vE R", then || u- v ISl u || +| v | (1

A: Solution

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

A:

Q: Prove that (i) Res (tan z, r/2) = - 1

A: Here,we have to prove that Res(tanz,pi/2)=-1

Q: Question #30

A: Note: Some of the basic calculations are directly written due to the question being very lengthy. We…

Q: Let X= Ucy) out of standard er dere d unierm and Y= Uc5) out of

A: From the given information, X=U(4) out of 8 standard ordered uniform and Y=U(5) out of 8 standard…

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: Prove that fdr %3D dSxVf

A:

Q: what expressi on is equivaient to this. (n-a)!

A: n!(n-2)!+n=n×(n-1)×(n-2)!(n-2)!+n  [we use the idea of factorial]=n(n-1)+n=n2-n+n  [distribute n]=n2

Q: Prove that (u + v) · (u - v) = llull2 -llvll2 for all vec­tors u and v in Rn.

A: Consider the given Vector equation, u+v·u-v=u2-v2 Here the objective is to prove that the…

Q: a- if w = f(u, v), u = x + y, v = x-y Prove that = ( - )* aw aw %3D ду du.

A: