1) The proper ideals of 7z is a) { o, 2, 43 b) fo,1, 3,5} c) to}i d) [o,1.2, 3, 4.5,6 }

Q: 11) lim [6-x| 11) x -6 6-x A) 1 B) Does not exist C) -1 D) 0

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Q: Find the calculation value of the bo coefficient Standard error coefficients 2,078 1,554 0,438…

A: Given,

Q: 56. Find U₁A, and A; if for every positive integer i, a) A = {i, i+1,i+2,...}. b) A, = {0, i). c) A₁…

A: According to guidelines we can solve only first three subparts.

Q: If x, y, z are integer's numbers and if x \y then x \ z then: 1) Show that x \ ym – zn for m, n e Z…

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Q: If x, y,z are integer's numbers and if x \ y then x\ z then: 1) Show that x\ ym - zn for m,ne z 2)…

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Q: 5) Expand using special product rules c) (12 – 4x)? d) (3y – 6)2

A: c. Given: Apply special product rule in the above expression.

Q: 5. The number of elements of Z3[x] / is а) 3 b) 6 c) 8 d) 9 O a) O b) O c) d)

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Q: 4 to onabans ! (0)0 4. Prove that

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Q: If x, y, z are integer's numbers then: 1) Show that if x \y then x\ yz 2) By use part 1 show that if…

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Q: 3x2 + 7x – 2 7) lim x-1 3x²- 4x – 2 7) A) 0 B) Does not exist 8 D) -

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Q: coprime

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Q: Find the values of w,x,y and z in fraction form using a)gauss elimination, b) gauss-jordan…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: One of the following sets is connected set: a) Qº The set of irrational numbers b) Z The set of all…

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Q: 2. Let Z [√2] = { a+b√2 la,be Z}. Define addition and multiplication on Z[√2] as follows: (a+b√2)+(c…

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Q: tind 16)790) Sorn that ha)=G0g)(x). Letg=2x+3 ha)= 3 12x43 11

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Q: let l X, BIR) be Boral mea sure 3pace Suppose that ŷ An- | otL sta be a family of elements of BIR)…

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Q: If x, y, z are integer's numbers and if x \y then x \ z then: 1) Show that x\ ym – zn for m,n e Z 2)…

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Q: Exercise 16: Write up three proofs for the above six theorems. (You should be able to do all of…

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Q: One of the following is an ideal of z1: (0,3} (0,2,4,6} None (9,3,6,9}

A: From given statement

Q: Theorem:. tet a andb be nenzero integers Then there exist Integers. r andd 8 Such that Hcf (9,b) =…

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Q: 5) A vng R is Called Boolean ving if.... a) x: y? Vx, Ye R b) x xy Vx, yeR c) None d) x:y vx, yeR

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

Q: Find the power set of: a) {w, {x}, {y, z}} b) {1,2,7} с) (3,(1,4)}

A: Given:-  {w, {x}, {y, z}}  {1,2,7}  {3,{1,4}} To find:- power set  of given sets

Q: 1. Specify the order of the zero z = 0 of the following functions: a) f(2) = z²(e* – 1), b) f(2) =…

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

Q: 1- The distance between two complex numbers z1 Z2 is denoted by: a) Iz – z2| b) /x + y c) Vz, + z2…

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Q: Which of the following is NOT true?    A.) If a is in R and a is not equal to 0, then a^2 > 0. B.)…

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Q: 26) lim √√x-3 x-9 x-9 A) -10 B) 1 6 C) -2 D) 5 16

A: we have to find limit.

Q: 4.a) Show that (1+2i) is a zero of the polynomial Qcx) = x²-6x*+3x -20. Hence , or otheruwise, write…

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Q: 1) The of 77 is proper ideals a) { o. 2, 43 b) fo, 1, 3,5} c) { o}i d) {0,l,2, 3, 4,5,6 }

A: Given :   Proper ideal of z7

Q: Let u, v E Z. Show using only the definition of a divisor and algebraic properties that if 7|u and…

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Q: = 36 ala,beZ}and let ø : R → Z be a mapping defined by : [a b -6. b

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. Prove that the Cartesian product N Nis countable

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Q: Give 3 different examples of norms on R

A: In (1) and (2) same question is written. Here solving 3 different examples of norm on R. If you want…

Q: 5. Find U₁₁ A; and ₁ A; if for every positive integer i, a) A¡ = {i, i + 1, i + 2, . . .}. b) A¡ =…

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Q: 1. In Z[i], 1+2i and ___ are associates a) 2+i b) -2-i c) 2-i d) 1-2i e) none of the above 2. What…

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Q: 10. When dividing x* + 3x? + 2x + 1 by x² + 2x + 3 in Z5[x], the remainder is а) 0 b) 2 c) 3 d) 4 a)…

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Q: SEQUENCES AND SERIES ALGEBRA II 28-1 (THOMAS WILLIAMS, ID: 12390719) Warning: if you leave this…

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Q: 2 If A =-2 1 +1 2 2+1 1 8 7 5 4 -3 and D is the adjoint of A then D is: 9 1-31 A) 9-1 E) 85 + 111 B)…

A: Option D is correct answer. Here is solution.

Q: If x, y, z are integer's numbers then: 1) Show that if x \y then x \yz 2) By use part 1 show that if…

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Q: 1. xx 2. 54 3. 4. 2x(4x-7) 5. 8° 6. (x) 7. x.x*.x 8. (4x')

A: 1 - AD         2 - C 3 - BC          4 - ACE 5 - D            6 - BD 7 - AE          8 - ABC 9 - BE…

Q: Problem 67. a) Prove that there are infinitely many positive integers m, n such that √3m + 3 EN b)…

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Q: Show that S = {a+b√2+c√4 | a, b, c = Z} is a subring of R.

A: Here we have given a set,