b) Prove that if x

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Q: Find all solutions of y" = ln x

A: We have to the differential equation.

Q: а. v(Ã ·) = Ã × (V x B) + B x (v x Ä) + (Ã ·v)Ē + (B · V)Ā b. · (Ã × B) = B · (v × Ã) – Ã · (V × B)…

A: Part(a): ∇A⇀·B⇀=A⇀×∇×B⇀+B⇀×∇×A⇀+A⇀·∇B⇀+B⇀·∇A⇀ From the left-hand side of the given equation,…

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Q: . Let C = {0, 1, 2, 3} and f : C → C, g : C → C with f = {(0, 2),(1, 2),(2, 3),(3, 0)}, g = {(0,…

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Q: Define relations S and R on the set A = {x, y, z, w} as follows S = {(y, x), (x, w), (w, z), (x,…

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Q: Let A = {1, 2, 3, 4} and let f:A ->A be defined as {(1, 3), (2, 4), (3, 1), (4, 3)}. Is f…

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Q: 2. Answer the questions with Yes or No, and then explain why yes or why not. Justify your answer. a)…

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Q: Let A = 1 -X -X X 1 -x X X -1 Find x such that A is invertible.

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Q: b) A function g:Z→Z is defined by the rule g(m, n) = m + n Determine whether it is onto or not...

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Q: Let u, ER" prove that ||ū + ï|| ≤ ||ū|| + ||v||

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Q: Let R be a U.F.D. and F its field of quotients. Then fo (x) any f(x) e F [x] can be written as f(x)…

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Q: Let A = (1, 2, 3, 4, 5) and B = {a, b, c) and f = {(1, a), (2, a), (3, b), (4, b). (5, b)}. Choose…

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Q: Let X = {o, p, s, w}, Y = {a,b, e, g, k}, and Z = {1, 2, 3, 5, 7, 9}. Let ƒ : X → Y where f = {(o,…

A: X=o,p,s,wY=a,b,e,g,kZ=1,2,3,5,7,9f:X→Yf=o,a,p,g,s,e,w,bg:Y→Zg=g,3,e,2,b,9,k,7,a,1

Q: (2) Suppose that G, C Zn-r. Then prove that G,-1C Zn-r+1

A: We prove that

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Q: Let X be a pre-Hilbert space then [(x, y)|

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Q: Show that if f : A → B and g : B → C are one-one, then gof : A → C is also one-one.

A: To show that the composition of two one to one function is also one to one.