I see that parts 1-3 are answered but can you help me with 4-6?

Q: (b) Prove that Z/4Z is not a field.

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A: Given, f(x) := x² for x∊ R,  E := {x∊ R : -1≤x≤0} and F := {x∊ R : 0≤x≤1}.

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Q: 5. Consider X with the discrete metric. (a) Show that every subset of X is open and closed. (b) Show…

A: Consider X with the discrete metric. (a) Show that every subset of X is open and closed. (b) Show…

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Q: Find the f(t) for te-3t e-3t te-6t 1-te-3t F(w) = 6w (9+w²)²

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Q: Exercise 11. Recall the following Example of a topological space with the real line as underlying…

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Q: Show that if f: A→B and E, F are subsets of A then f(E∪F) = f(E)∪f(F) and f(E∩F) ⊆ f(E)∩f(F).

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Q: 1) A) Show that the set of all odd integers is countable, by producing a 1-1 Function F From J onto…

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Q: 1. 2. n−1 4 nh+n-6 7n+1 n² +1

A: We shall divide and using the highest power of n and then find the limit

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Q: Problem 1 Consider the set A of all strings of letters a- ● dcbac eba fe aba fa ● ● f of length 5.…

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

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Q: Refer to the table below. Of the 36 possible outcomes, determine the number for which the sum (for…

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Q: & (in/in) fps (ksi) 0.01 230 0.02 255 0.03 260 0.04 264 0.05 268 0.058 270

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Q: Write it again

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Q: (c) Prove that the set of congruence classes modulo m is a commutative ring.

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Q: Prove that 1^2 - 2^2 + 3^2 +...+(-1)^(n+1)n^2 = (-1)^(n+1)n(n+1)/2 for all n∊N.

A: We will prove the given result by principle of mathematical induction.

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Q: Find the nullity(A) and a basis for the null space of the given matrix. (If an basis for the null…

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Q: Consider the matrix A given below. . . A = Determine if x = 0 -1 0 1 0 6 2 3 5 10 -10 - -6 is an…

A: Consider the matrix A given below.A = [[0, - 1, 0], [- 6, 1, 0], [6, 2, 3]]Determine if x = [[5],…

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Q: B. Express the ff atticher whit with general Form quadortic function. 1. 2 9=C++3) ²-3 FLAMU

A: The general form of a quadratic function is

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A: Given that C1 is the curve parameterized by r(t)=(cos2⁡t,sin⁡t),t∈[−π2,π2].Let C2 be the line…

Q: Prove there is no real number x such that x8 + x6 + 1 = 2x³.

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