Fin d the Zero divisor of the to llowing ring s 2) 8.

Q: - 21 , Prove that + (n? m' ) yn=o 2.

A: According to the Leibnitz theorem, dndxn(uv)=C0nunv0+C1nun-1v1+C2nun-2v2+... Formulae used:…

Q: Show that if a and b are positive integers, then there are divisors c of a and d of b with (c, d) =…

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Q: 4.In AABC, BX bisects ZABC. a. If AB= 10, BC = 8 and AC = 12, find AX and XC. b. If AX= 5, XC = 7,…

A: We will solve the given questions of the given triangle ABC  in the following step.

Q: Suppose an -6a, 1+ lan 2 - lan 3 and a4 34, as = -211, and as 1305. Find a1, a2, az. %3D %3D and

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Q: For two R-modules Mand N Show that Hom (M,N) any with the composition is not agroup?

A: Given that M and N are two R-modules. We have to show that HomM,N is not a group under composition.…

Q: For circuit M, find out what orders its nonzero ones have elements and find their divisors of zero,…

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Q: Construct a proof that ZEIF = ZGIH. н

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Q: 3 2 If A = use the Cayley-Hamilton theorem to determine A?. 5 1

A: We can solve this by using given information

Q: If "C, = K "C,, then K is n-1 %3D

A: Combination problem....

Q: Find ||uLy|| in Figure u= (3, 5) = (8, 2) P. FIGURE

A: v=(8,2) u=(3,5) uv=?

Q: 2. Assign Hermit's interpokting tolynomial by The fallowingy da ta:

A: The Hermite's interpolation polynomial is H(x)=∑ui(x)⋅yi+∑vi(x)⋅yi'. Here…

Q: Prove: Vn, meZ,if n and m are odd, then n-m is even

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Q: S. Gives 4. Prove mADC-ABC D.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: In ([0, о), т оос), if A %3DN, then A'%- Оа. А-{1} O b. [0,0) О с. (0, о) O d. Ø О е. А

A: ( [0, infinity) , Tcoc)  Since it is Co-countable topology. All countable sets are closed in given…

Q: 2. Suppose A is an m x n matrir, x ɛ Rª and Ax = b. Then b is in 1) R" | 2) R™ 3) RmfnT 4) R™n

A: Given :  A is an mxn matrix , x∈Rn and Ax=b   To find :  b is in which space of the given spaces.

Q: Determine for which n ≥ 3, Wn has a Hamilton circuit. Justify your answe

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Q: 3. cooficiant af z" in the apransion 3)11

A: From the Binomial Expansion

Q: If OE = OF, then AB 2 CD. %3D

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Q: you to If ZA ZD and ZC ZF, which additional statement does NOT allow conclude that AABC = ADEF?

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Q: 37 17 Squeceze theorem to 8how an= 3" Conuerqcnt, Use aveeze

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Q: ) If In(a) = 2, In(b) = 3, and In(c) = 5, evaluate the %3D ollowing: -1 a a) In b-4c! 5) In Vbºca¬T…

A: Answer (a):   lna-1b-4c1= ln(a-1) - ln ( b-4c1)                                            =ln(a-1)…

Q: 2) of Ec, 4" is convngend can we conclude that coch of these are comvergent: (4)

A: Given The sires is convergent 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: Prove: Vn,meZ, if n and m are odd, then n-m is odd.

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

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

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Q: Verify S Tokes' Theorem To 2.

A: Introduction: We know that stoke's theorem is given by the formula, ∮CF.dr=∬s2∇×F·n.dσ

Q: If In a + In(z-7) = In(4x), then z = 11 %3D

A: Since you have posted more than one question we solved the first one for you. For the remaining…

Q: in= aRo can direetly /KT. by gomma fometion, We write Jo a Kox2 &KT 2

A: If you have any doubts in the solution please ask me  in comments i will reply you as soon as…

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: Cannot solve!

A: Given complex numbers are These can be written in polar form as Now,

Q: v. Let Ac S, prove that P(Ā) = 1- P(A)

A: Given that

Q: Explain why the funclion (2)3D 12)=52-6+zcos Z-Ze is. entire ?

A: Answer

Q: Let 9= {[a,b]: a,bER}, then 9 is Borel algebra

A: TRUE ;

Q: 33, A Sphene has the iengen of t

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Q: Prove the soquen enat 2efin ea For n EIN Conv e

A: Introduction: When each term of a sequence is greater than its previous term, the sequence is…

Q: 32, as 185, and a6 = 1121. Find a1, a2, 5an-1+ 6an-2+ lan-3 and a4 Suppose an and a3-

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Q: 11. Show that dza;b; is equivalent to a b. ij

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Q: (5) The ring (Z,,+6,6 ) has that rad Z, = %3D .... .. (a) ((0), +6, -6) (b) ((2), +6. 6) (c)…

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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: In AJKL, JL is extended through point L to point M, MZLJK = (x + 9)°, mZJKL = (x - 2)°, and m/KLM =…

A: The exterior angle is equal to sum of two opposite interior angles. We will use this property to…

Q: -show that. Z, ax Rings.

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Q: (b) Show that when dist(x, y) = dist(x, –y), then x and y are onal. orthog- %3D

A: Given  dist(x,y) = ||x-y||

Q: If A subut of B. where B 18 a closo d subset of IR show that

A: Given: A is a subset of B, where B is closed subset of ℝp. To show: A¯⊆B.