Prove: If f € R(a) on [a, b] and if |f(x)| < M on [a, b] , then | S. f da| < M[a(b) – a(a)].

Q: For a function f: A → B and subsets C and D of A, prove that f(CUD) = f(C) Uƒ(D).

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Q: For S in the domain of f, let f ( 5 ) = { f(x): * € S}. Let C and D f de subsets of the domain of f.…

A: S is in the domain of f fS=fx: x∈S Let C and D be subsets of the domain of f Then we have to show…

Q: (c) For any (a, y) E R?, let F(x, y) = (4x - 3y + 1, 3x +4y + 1). Then F is a similarity.

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Q: Let g : B → N × N where BCZ given by g(m) = (|m| + 2, |m| + 3). Choose all subsets B such that g is…

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Q: Let g : B → N × N where B C Z given by g(m) = (|m| + 2, |m| + 3). Choose all subsets B such that g…

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Q: Prove: If f1, f2 € R(a) on [a, b] with fi < f2, then ' fi da < s' fz da

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Q: What is true about the function -- asx-m? OAM-f B) (x) 0 from below OC) f(x) is undefined OD)x) from…

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Q: (b) ƒ(AnB) ≤ f(A) Ñ ƒ(B)

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Q: Suppose that A,B⊂S such that Pr[A|B]=25, Pr[A]=12 and Pr[B′]=12. What is Pr[B|A′]?

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Q: Let f, g be entire functions such that f(z)| ≤ lg(z)| for all z E C. Show that there exists a cEC…

A: Given that f and g are entire functions such that |f(z)|≤|g(z)| for all z∈ℂ. We have to show that…

Q: 1. Define function f : Z+ → Z such that f(n) = /n. (a) Is f one-to-one? Justify (prove) your answer.

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Q: If f, g E R[a,b] with f < g on [a,b], prove that g.

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Q: 7. ) Let f: N→ Z with f(n)=n+4. Let A = {1,2,3} and B = {1 € Z \ I <10). Use these to find the…

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Q: Prove: If ƒ e R(a) on [a,b] and g e R(a) on [a, b] , then fg e R(a) on [a,b]

A: Given if f∈Rα on a,b and g∈Rα on a,b. We have to prove that fg∈Rα on a,b. Since, f∈Rα on a,b then f…

Q: Prove: If f₁, f₂ € R(a) on [a, b] with f₁ ≤ f₂, then so f₁ da ≤ f f₂ da.

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Q: 8. (p f(A) ≤ f(B), then ACB. Let f: XY. Prove that for all A, B C X, if f is one-to-one and

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Q: Let f:2+ +2 be the function defined by if n>l00 f(f (nt 11)) othe rwise fln) =d n-10 what is the…

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Q: Show that the function f: N² → Z given by f(m, n) = m²-n² is neither injective: suriective. nor

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