Prove that the chromatic number of G is 4. Ie: x(G) = 4.

Q: Prove or disprove: There exist two connected graphs G and H both of order at least 3 and neither of…

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Q: Find the z tronsfom of f(n) = a" cos (bn).

A: We have to find the z transform of the following.

Q: An example of a partition of the integers is E Z}

A: Set of integers is defined as {... -3, -2, -1, 0, 1, 2, 3,....}. A partition of a set is defined as…

Q: Which numbers satisfy lal = a? Which satisfy lal = -a? What about I-al= a?

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Q: The Canonical form of a hyperbolic PDE is Ugn = F (§, n, u, ug, un)

A: "TRUE" The pde is hyperbolic (or parabolic or elliptic) on a region D if the pde is hyperbolic (or…

Q: ii. Show that the image of the hyp n2 = cos2n

A: Introduction: Inversion and Reflection: The transformation is w=1z.

Q: Find k such that 2x = ekx for all x.

A: To find k 2x=ekx

Q: Derive the canonical form of the given parabolic PDE (b) - 3u. +64.- 3u = cos(x).

A: given 2nd order PDE -3uxx+6uxv-3uyy=cosx   ...i claim- to derive the canonical form of given PDE

Q: 15) Find The natural domain (a) fx) =3 os X 6 g0) = ©dix) = Sin? x O ra) = 19-x2.

A: given(a)f(x)=3cosxdomain of this function is (-∞,∞)(b)g(x)=13+xx≥0therefore domain is [0,∞)

Q: Write Taylor Polynonial at, x = &f degree 4 estinating 6)= ex and ex %D or 1o,2]- Graph Py (x) @…

A: The Taylor polynomial of a function f(x) at a point a is given by .

Q: Let A = psino a,+p a,. Evaluate A dl given that L is the path shown in the figure. 1. Verify your…

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Q: On an elliptic curve E in the group F37 the point P is (21,23). What is the point -P?

A: Some facts :-Fact 1 : In an elliptic curve group , the negative of a point Px,yis its reflection…

Q: The characteristic of Z6 x Z, is 18.

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Q: This exercise refers to the triangular symmetry group discussed in this section.Which element is the…

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Q: Let G=(V, E) a graph, then show |{ € V\dg(x) = 1 mod 2}|= 0 mod 2.

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Q: spectra of TT* and T*T are real and cannot

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Q: 1. Find the 2 transformations that occurred to map quadrilateral KLMN to quadrilateral K"L"M"N" in…

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Q: Suppose f (x) =x²csc²(x³). Evaluate: A - 3cot(x³) + C B -con(x*) +C © -x²cot(x³) + C O -co(x*) + C

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Q: By sketching the appropriate loci on an Argand diagram, find the value of z that satisfies |z|=13…

A: For the solution follow the next step.

Q: 3. For any graphs G and H, the ringsum G@H is empty if and only if E(G) = E(H). %3D

A: Let G and H be any two graphs. Let VG, VH denotes the vertex set of graphs G and H respectively. and…

Q: Notice that h is definec this.)

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Q: Suppose that E is an extension of F of prime degree. Show that, forevery a in E, F(a) = F or F(a) =…

A: Let E be an extension of F of degree p (prime) => [E : F] = p Here we will use tower property to…

Q: G Given: AT GS, AT || GS 5. A Prove: AGAT = ATSG

A: We will use congruency in triangles

Q: Prove that for all values of the constant A, eAInt = e In.

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Q: 3. The following two graphs G and H are isomorphic. List all the isomorphisms from G to H. G: H:

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Q: - [: ]} а b Identify all of the nonempty submatrices of A d

A: →A matrix obtained by deleting some of the rows and/or columns of a matrix is said to be submatrices…

Q: Prove the following combinatorial identities (algebraically): (") = Eo ("*) 1) ("") = E, () (") 2)

A: We have to prove thatm+n+1n=∑k=0nm+knProof⇒ As L.H.S is number of subsets {1,....,n+m+1} of size n…

Q: z has a power (z) is

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Q: Suppose that f: G → G such that f(x) = axa?. Then f is a group homomorphism if and only if O a^4 = e…

A: Given that f from G to G is a function defined by f(x)=axa2 Then we need to find a necessary and…

Q: Let be an element of f a that d=g Group and x5 =e, Then G Such solve for I %3D terms of 9. in

A: Given that  g be an element of a group G such that x2=g and x5=e. Then we have to find x in terms of…

Q: Give an example of two denes not equal X subsets of (R,Te) and (z, cof). ( Explain your answer ).

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Q: The characteristic of Zs[x]/ is 6. O None of the choices

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Q: Use the definition of limit complex function to find 8-e, for which lim(3z + 2) = 3i +2. O (A) 8=…

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Q: Find the representation B of L with respect to S' and T'.

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Q: to following a 1-tan B. tal

A: Here we have to prove that ,  tan(A+B+C)=tanA+tanB+tanC-tanAtanBtanC1-tanBtanC-tanCtanA-tanAtanB

Q: 3. Let A : - ® be given by T2 In A(x1,..., Tn,.) = %3D 2 22 a) Prove that A is compact. b) Find the…

A: Given linear operator A:l2→l2 is defined by: Ax1,x2,…,xn,…=0,x12,x222,…,xn2n,…. (a). We Know that…

Q: Prove that for every y E R, there exists a unique x E R such that 2(x – 1)3 – y = 0. %3D

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Q: 7. Prove there exists a unique x E R such that for every y € R, ту + т — 2 3D 2у.

A: We have to find the unique value of x for which the given equation is valid. We have, xy + x -2= 2y…

Q: Find all the generators tof the subgroup H = (2) in Z24-

A: In any cyclic group of order n has phi(n) generators. We use this technique to solve the problem.…

Q: For any x E R, there exists n EN such that x < n; ylgn ihi

A: We have to state whether given statement is true or false.

Q: 5. For A = {a %3D identity fune

A: As per the company rule, we are supposed to solve only one problem. Therefore kindly repost the…

Q: Let co be the space of all sequences of complex numbers that converge to 0, that is, co = {f: N → C:…

A: Let c0 be the space of all sequences of complex numbers that converge to 0. c0=f:ℕ→ℂ:limn→∞fn=0…

Q: By algebraic properties of R, prove that for every x, y € R with y # 0 (-x) y

A: We have to prove that by algebraic property that ∀x,y∈ℝ with y≠0 -xy=-xy

Q: Find the inverse Z-transtorm of he follows housing de X(Z)= tanh (z

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Q: Q3- Give an example of two denes not equal X subsets of (R,Te) and (z,ror ). ( Explain your answer…

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