By using the fact that P[AU B] < P[A] + P[B], show that P[AUBUC]< P[A] + P[B] + P[C]. By using the fact that P[U- Ak] < D, P[Ak], show that P[N-1 Ak] > 1 –Ei=, P[A£].

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Q: and H since L'et 18) His normal (9) G is cyclic since

A: Part(8) We have G=ℤ6 and H=0,3 Now, G=ℤ6 is a group.   Every subgroup of an abelian group is normal.…

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A: The solution are next step

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Q: 1d) Prove: If z=Zo is a zero of order n of flz), then it is zero of order 2n of

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Q: 4 Lonsider the functlan fx)= -5x4- |l+x?tx-17. functfon Fex)= -5xH-|l+x²+2x-17. 5xH-113+ Whatis r n…

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A: We will find out the required value of g(t).

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Q: find the poin ts of discontinuity of the following func tion s : (a) g (x,y) %3D (b) f laiy)

A: g(x,y) = 11-x2+y2The point of discontinuity is where g(x,y) approaches ∞. Or the denominator of RHS…

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A: Given that: 1. y=x2ex2. Graph of f(x)

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Q: Find f such that the given conditins are satisfied.  f'(x)=5x^2-7x+4, f(0)=2

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A: Now, it is given that ux(0, t) = 0   The D-Alembert’s formula is given as:

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Q: Let f(x) = 2x +3, g(x) = x – 4, and h(x)= 4x – 1. Compute (h o go f)(3).

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Q: T be the lineas translfomation et whose standasd matsine is A= 2 -2 2. - 2 Does T maps 3 3. R4 onto…

A: A=2-29203-230005

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Q: AE Mmxn amed suppose be non Let that A=xY is the fall ragak factorization that At =x*y then Show

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Q: [1 0 1 2 0 -1 Find a mat rix P such that P- 0 -1 [10]

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Q: inf f, is not measurable Vn. Isisn ulgn

A: False Statement

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Q: b) Find the largest possible domain A, where all elements of A are non-negative and f: A → R, f(x) =…

A: Solution:-

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A: Eisenstein's Irreducibility Criterion: Let us consider polynomial…

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Q: 5. Find all pairs (m, n) of positive integers such that y(y(nm)) = n, where p is Euler's totient…

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Q: Verify that f(x)=x2+1/x satisfies the hypotheses of the Rolle's Theorem on the interval [1/2 2] and…

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Q: For a function f(x) = peª + qe¬ª where p and q are non-negative real numbers such that p + q = 1,…

A: Provided function is: f(x)= pex+qe-x , p and q are non-negative real numbers and p+q=1 q=1-p. Value…

Q: 3. Find the generator of X = Xo + ut + oWt, where W is a standard BM, and identify the PDE satisfied…

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Q: Prove that for a > 0, the function

A: Introduction: The given function is:

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A: First find the derivative of the given function and compute the critical points.

Q: Define G : R R by the rule G(r) = 4r +3, for all real numbers z. ) Is G one-to-one? Prove or give a.…

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Q: Let f(x) is defined as (kx² – 1, S (x) = x-1 Determine k so that the fur

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Q: Verify that the hypotheses of Rolle's Theorem are satisfied for f (x) = x² – 12x + 35 on the…

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Q: Let g(x) = x². Which of the following outputs of g is not guaranteed by the Intermediate Value…

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Q: Find all the values of x satisfying the given conditio

A: Given:- y=x-√(x-2) To find:- value of x when y=4

Q: Consider f(x) = 2x +3. Is f : N → N one-to-one? Is it onto? Prove, or give counterexample.

A: As per our guidelines we can answer only one question. please repost other seperately

Q: Find the domain of gof, iff(x) =x² and g(x) = Vx-6. %3D O a.l-, - võJU(võ. x) O b. (-30, -6]U[6, ¤)…

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Q: Find a mat rixP such that P [1 2 1 0 | 1 0 P = O A. -1 1 1 - ОВ. 1 P= OC. 0 1 -1 0 P = O D. 1 1 1 0…

A: Just multiply both sides by P from left side and set P as 2×2 matrix.

Q: Find the linearization L(x) of f(x) at x = a. f(x) = 3square root of x, a = 27 show all work

A: fx=3x, a=27 Differentiating with respect to x, we get f/x=3·12x    ∵dxdx=12x=32x Now,…