The number of the Automorphism from Z30 Z30 O 28 O 29 O None of them O 30 08

Q: · Let m be given fixed positive integer. Let R = {(a,b): a, b E Z} and (ab) is divisible by m. Show…

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Q: 6. How many mappings are there from A to B where A={1, 2, 3, 4} and B = {Low, Middle, High}. How…

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Q: 2) Let R be aring. An element a6 R is called a Zero divisor if there exists bER Such that a) a.b=0…

A: Introduction: A ring R is an algebraic structure on which two binary operations are imposed. This…

Q: 3- o is а) Нomonorphism. b) Isomorphism c) Automorphism d) None O b)

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Q: %3D The members of the set {rx is an integer number such that r² = 2} are Оа. (2,2) O b. (-V2, v2) О…

A: To findElement of (say)A={x| x is an integer number such that x2=2}

Q: "m+nis 5. ( Let set A be the set of integers. For all m and n in A, mRn odd". Determine if the…

A: Given that A is the set of integers m,n∈ℤ, mRn⇔m+n is odd. a) Reflexive: aRa⇔a+a is odd, ∀a∈A b)…

Q: 2) Let R be aring. An element a6 R is called a Zevo divisor if there exists beR such that a) a.b =o…

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Q: Prove: |P(A)|= 2" where |A| = n. (Here P(A) is the power set of the set A with n elements.)

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Q: A. Convert the binary number 111010101.110111 to hexadecimal. B. Determine the power set of the set…

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 2) Let R be aring. An element is called a Zero divisor if there exi sts bER such that a) a.b=o E)…

A: Let R be a ring.An element a∈R is called a zero divisor if there exist b∈R such that _____

Q: Let a, b, c be positive integers. Prove that there exists integers x, y, z such that ax + by + cz =…

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Q: Let x={1,2,3,4} and y={1,2,3,4,5,6,7,8,9,10}   and "f" from X to Y is given by…

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Q: 6. How many distinct cosets are there in the factor ring Z[i] /3+i)? Explain your answer.

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Q: Z[i] is an integral domain with: O 9 elements 6 elements O 49 elements O 121 elements

A: Since 7 is prime, all the elements in {1, 2, 3, 4, 5, 6} are relatively prime to 7. So option  (B)…

Q: The set AcRis dense in Rif .A A =R .B A°=R .C (A)° = Ø .D none of above

A: Option (A) is correct.

Q: Let the operation on N defined by a*b=a-b, Va,beN. Then, find the property which satisfies by the…

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Q: J={all numbers of the form 3n + 2 , n as a natural number} is the set closed under multiplication

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Q: De ne function f : Z ! N by f(n) = 2n if n > 0 and f(n) = 1 ? 2n if n   0. (a) Observe that the…

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Q: Let Z* be the set of positive integers. We define the binary operation f:Z* x Z* → Q by f(a, b) = .…

A: The binary operation is defined from the cross-product of a set to another set. The binary operation…

Q: 20. Let B; = {x eR|0< x < i} for all integers i = 1, 2, 3, 4. a. B1 U B2 U B3 U B4 =? b. B1 N B2 N…

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Q: Let n be a positive integer. Let H = {0, ±n, ±2n, ±3n, . . .}. Findall left cosets of H in Z. How…

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Q: Let m be given fixed positive integer. Let R = {(a,b): a, b € Z} and (ah) is dixisible by m. Show…

A: To show R is symmetric relation

Q: Prove: | a + b | &lt;= | a |  + | b | for all a's in the reals.

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Q: Determine if the following statement is true or not. Let the domain be the set of all integers Z. Jx…

A: Set of all iintegers is: Z={0,±1,±2,±3,...}

Q: Which of the following are indeterminate forms? 00, 00, 0“, 1º, ∞* Select one: O a. 00, 0º. 0*, 1º,…

A: We will solve the problem

Q: Verify the combinatorial identity with a combinatorial argument. nCk ∙ n-kCj = nCk+j ∙ k+jCj

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Q: Shetch the snd e Yegion of Indegrstem evaluate the 2.

A: We have to sketch the region of integration and evaluate the integral.…

Q: 2) Let R be aring. An element a6 R is called a Zero divisor jf there exi sts bER Such that a) a.b=o…

A: Given: Let R be aring. An element aÉ R is called a Zero divisor if there exists bER such that

Q: Find the Boolean product AOB where A and B are defined below. [1 0 1 A = 0 1 1 1 1 0l [1 0 1 B = 0 1…

A: Here given that                           A=101011110       and       B=101010100 We have to find…

Q: let G be the set of all triples of the form (k1, k2,1) or (k1,k2,-1), where the ki, i=1,2 are…

A: Given :  G = k1, k2, ±1 : k1, k2 ∈ℤ with the operation  k1, k2, 1l1, l2, -1 = k1+l2, k2+l1, -1 To…

Q: Assume X = (1,3,5,7}, Y = (1,9,25,49)} and F(x) = x2, such that F:X Y. Then the following is true…

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Q: Let a, b,c be non-zero integers. Suppose that x, y are integers such that ax + by = c. (i) Show that…

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Q: (6) Suppose A CR is countable. Show that there exists a real number r such that An(r+ A) = 0. (Here,…

A: We prove this by contradiction

Q: 3) Let II" , m i=1 where p1 0 integers. Show that d eN is a divisor of m if and only d = II p§ª…

A: Prove the theorem.

Q: Hiwi! Find All Automorphism Y:( -cu 4 4 ما 3

A: C4 is the cyclic group of order 4 and we know that every cyclic group of order n is isomorphic to Zn…

Q: 2. Using the result above, show using induction that, if R is a relation on A, then R" o R = Ro R"…

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Q: Which of the following is isomorphisma f: (R, .) → (R, .) where f(x) = Inx this option O None of…

A: Lnx is not a function and second ome is not onto

Q: Using exclusively induction, prove that, if X, X1, X2, . . . , Xn are sets, then X ∩(X1 ∪ X2 ∪ · · ·…

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Q: a * H is a set of coset. O None of them O left O right O sub O semi

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Q: (b) Define an operation on our construction of the integers by [(a, b) [(c, d)) = [(ad, be)] for all…

A: Defining the operation * on the set of integers by  a, b*c, d=ad, bc , where a, b, c, d∈ℕ To show :…

Q: A. Convert the binary number 1010101101001.1110 to hexadecimal. B. Determine the power set of the…

A: A. Given number is binary form is 1010101101001.1110 Make brackets for 4 digits…

Q: Let G = Express b2abab3 in the form biaj.

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Q: Check that p is a representation of V. (i) (ii) Find the character of p. (iii) Is p irreducible ?…

A: Given: Let ρ:V→GL2Cρe=1001ρa=-1001ρb=-100-1ρc=100-1

Q: Use Green Theorem to Evaluate y x²dx – x²dy where C is left half of x² + y² = 25 Other O 77.7704 O…

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Q: Determine all natural numbers a, y and z such that z < y < z, and xyz + zy + cz + yz+x + y+ z+1=…

A: Given, xyz+xy+xz+yz+x+y+z+1=2020 (xyz+xy)+(xz+x)+(yz+y)+(z+1)=2020 xy(z+1)+x(z+1)+y(z+1)+(z+1)=2020…

Q: Let G = Express b3abab3a in the form biaj.

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Q: a) Find the number of positive integers not exceeding 120 that are divisible by 3 or 4. 1 0 01 0 0 0…

A: As per our guides lines I answered only 1st part

Q: Let D CC be a domain, BCD an o that BC D. If f is holomorphic in D (f(B)) of f(B) is contained in…

A: Holomorphic function: A holomorphic function f was defined as one that does not contain the letter z…