Explain which of the following is the ideal of Z × Z.   a) {n,n:n∈Z} b) {5n,0: n∈Z} c) {m,n: m+n even integer} d){m,n: m.n even integer}     e) {(2m,3n):m, n∈Z}

Q: Let ū = (-1,2,4) and ū = (-3,5, 2). Compute the following: (a) ū+ū (b) .공 (c) ||해 (d) ũ - 7 (this is…

A: (a) Find u→+v→ as follows: u→+v→=-1,2,4+-3,5,2          =-1+-3,2+5,4+2          =-4,7,6

Q: HW 2: If Z - N(0,1), find a) p(Z > 1.2) b) p(-2 <Z< 2) c) p(-2 <Z < 1)

A: If Z~ N(0,1)   which means clearly it is standardized normal distribution table.

Q: For aib E 2, let d=ged (2a tb, 3a+2b) la) Prove d is a common dliusor of a & b (6) Prove, d is the…

A: Introduction: The number c is a common divisor of the numbers a and b if and only if c | a and c | b…

Q: 4. Prove for A = {x: x = 12k, k = Z}, B = {x : x = 3k, k = Z}, and C = {x: x = 4k, k = Z} that A…

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Q: 1. Prove the cancellation property of addition (If x+ z=y+z, then x =y). 2. Prove: += ad/bc. 3.…

A: "Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: Submit through Canvas as indicated. T u = (2,-5) and v= −3i+7j

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Q: [t +3 If A = -1 6. t- 3 -6 one of the following must be true? 1 t+ 4] A) The rank is 3 ift#-4, B)…

A: Rank of the Matrix, and it's properties

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: 2) Let R' real numbers, define = x,Y1 + 3x2y; + 5x3y3 for x = (x, X2, X3) and y (y,Yz, Y3). Is…

A: Given x=x1,x2,x3, y=y1,y2,y3 in ℝ3. Define x,y=x1y1+3x2y2+5x3y3

Q: Let U(-5, -4, 3, 4, 6), V(-4, 1, 7, 1, 0). Find the inner product U.V

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Q: 7. 2) Write the difference equation for the systems shown below. ii) Find yon) / xen). yon) x(n) 3…

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Q: 1) Use "Colone Technique" to find x = 20+20+/20+... %3D A) V20 B) V23 C) 6 D) 5 2) Use "Colone…

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Q: a.) Give e a جا b.) Give

A: We use different techinques for solving this problem. The first one is quite easy and we make use of…

Q: Find the infimum and supremum of the set X = {3 – Vztn ine N}. -

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Q: Let f AB, prove the following: (a) if S, T are subsets of A, then f(SNT) ≤ f(S) nf(T); (b) if U, V…

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Q: gcd(a,b) = (a+b, lcm(a,b))

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Q: 5. a) Let V₁ = H b) Let V₁ = 11 ----- = V3 Does (V1, V2, V3} span R¹? Why or why not? Does (V₁, V2,…

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Q: Suppose p(x,y)=2x+y/33, x = 1, 2, 3, y = 1, 2 is the joint pmf of X and Y. Determine P (Y = 1). a)…

A: P(Y=1)=?

Q: a.) Ker(p) and p(24) for p : Z → Z7 such that Ф(1) %3D 4 b.) Ker(p) and p(16) for p : Z → Z10 such…

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Q: Prov that Let A be a fuzzy ideal of R, anand by Lemma- be fuzzy singletons. Then (a.b) no A = anobu…

A: To prove that (a⋅b)h ⋅A=ah ⋅bh ⋅A given A is a fuzzy ideal of R and ah , bh are fuzzy singletons, we…

Q: 5) Again let Universe U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Let S = {0, 1, 2}, T = {1,4}, R = {2, 4,…

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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: 9) 28 35

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Q: Q: Let z = -4 V3 – 4 i %3D A/ Find the following : 1) Iz| 2) arg (z)

A: Since you have posted multiple questions but according guidelines, we will solve first question for…

Q: If P and Q are represented by the numbers z1 and z2 such that H- then the circumcentre of AOPQ,…

A: Given P an Q are represented by the numbers z1 and z2 such that |1z1+1z2|=|1z1-1z2| We need to find…

Q: Let W = {(x, y) E R² : x, y > 0}. Define addition + of any two elements (x, y), (w, z) E W by (x, y)…

A: Let u=(x,y) and v=w,z be any two elements of W, where w,x,y,z&gt;0. Use the definition of addition…

Q: Which of the following is a TRUE statement? O A) C-1 = t6 O B) L-1 3 = 3-3e C) 6! = t (s+4)5 s2 + 5s…

A: Here we remind the formula of Laplace transformation of different functions. At the last we found…

Q: În a ring R, show that i) Oa = a0 = 0 ii) a(- b) = (- a)b=- (ab).

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Q: a) Let Z = 7 – 13i, find: i) Im ) ii) (Re Z)?

A: Complex Numbers: The complex number is basically the combination of a real number and an imaginary…

Q: 3. If y x +2 and u = 2x -1 then %3D du a) x b) 1/x c) 2x d) x/2 e) None of the above answers

A: Given that y=x2+2 and u=2x-1To find dydu

Q: 1.) Does the following set of polynomials {t2 +1,t? +t,t + 1} span P2?

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Q: Cietni let ane let G4)= ti t2+34)j +4K HIC4) = 2,4し + 34j+(-144)1k fnd の) H4)XG(H) b) G4). HG4)

A: Given: Gt=ti+2+3tj+4kHt=2ti+3tj+-1+2tk

Q: 2. X and Y are 3x3 matrices. |x|=-2 |y/= 3 (detarmenands) こ? A) 81 B) -81 C) 3 6 D) - 36 E) NOWE…

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Q: Let A={2,y,z} and B={3,x,z}. How many distinct elements are in (A×B)∩(B×A)

A: Given, A={2,y,z} B={3,x,z} How many distinct elements are in (A×B)∩(B×A) ?