9. Suppose that an experiment is performed n times. For any event E of the sample space, let n(E) denote the number of times that event E occurs and define f(E) = n(E)/n. Show that f() satisfies Axioms 1, 2, and 3.

Q: 7. (10 points) Let f: A B be onto. Prove that S((C)) = C for all sets CC B.

A:

Q: 7. If F{f} = [1, 1+ i, –2i, 2i, 1– i] then compute F{f©f}.

A:

Q: (e) If each fn has at most a countable number of discontinuities, then f hasat most a countable…

A: Consider the example: fnx=1q             x= pqwith p,q∈N, gcdp,q=1,q≤n0             otherwise So,…

Q: 3) Given the function f(x) defined by the table below, 1 4 2 8 b) a) Evaluate f(6) Solve f(x) = 4 c)…

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Q: 1. let the universe be all the positive integers (N). Determine whether the following are true or…

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Q: A 1. What is (go f)(x) if f(x) = 2x + 3 and g(x) = ? %3D O (go )(z) = + %3D O (go f)(x) = + } %3D O…

A:

Q: 8. (13 points) Define f: ZZ by f(n) = 5n - 5 for all integers n (a) Is one to one? Prove or give a…

A: Step 1:Step 2: Step 3: Step 4:

Q: (b) Let {Ai e I}. Prove that 4) =UA;. |A, iel

A: We need to prove that ∩i∈IAic=∪i∈IAic  for set Ai/i∈I We will prove using the following method: To…

Q: 1. (10 points) Consider the set 2020n + 2021 S = :n = 1,2, 3, n+1 Find sup(S) and inf(S) and…

A: Since you have asked multiple questions, we will answer the first one. If you want other questions…

Q: Dijec not need to prove you function is a bijection): (a) N and Z (b) Rand (1, ∞) (c) (0, 2) and (3,…

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Q: Question 5. Consider the following three statements about a real number x: • P(x): -1 ≤ x ≤ 3. •…

A: P(x) : -1≤x≤3 Q(x) : x2 > x  x2 > xx2 - x > 0x(x-1) > 0x > 0 and x - 1 >0 ⇒ x >…

Q: F (8)

A: We are given setsWe have to answer (d), (e), (f) and (g).

Q: 20 - If f is a function on a set A= {1,2,3,4,5} such that f= { (1,2), (2,3), (3,4), (4,x), (5,5)}.…

A: Use the property that in bijective functions each element of doamin and codomain has image and pre…

Q: Which of the following is a critical number of f(x)= 4. 2x %3D

A: The given functIon is: f(x)=14x2-2x

Q: And Justify True OR False f(a, b) = (a-2)² + (6-3)³. Then, we say Pornt (2.31 T f=R²-)R. is local…

A: Given                                                             The stationary point is

Q: prove that each wff is a valid argument. (∀x)P(x) ^ (∃x)[P(x)]′ → (∃x)Q(x)

A: As per the question we have to prove that the following wff is a valid argument : (∀x)P(x) ^…

Q: a_ if f(z) is analytic function, show th 2 8²) | f (2)| = + | f (2)| ² 78 Dy12

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Q: Suppose f: R → R is defined by the property that f(x) = x + x² + x³ for every real number x, and g:…

A: We are given that, for all real number x,          f(x) = x + x2 + x3  And        (g o f)(x) = x…

Q: 3. Let h: Z→ Z be the function h(r) = = x mod 4. Find h-¹(0), h-¹({0, 1, 2, 3}), and h-¹(4). Explain…

A: In this question we can easily observe that that output of the function is the remainder when any…

Q: •ffe -32²-3y² dA; R= {(x, y)\x² + y² ≤ 4, x ≤ 0,y>0} R 4. (Section 16.3) Evaluate

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Q: 9x 9* +3 Let f(x) = evaluate Show that f(x) + f(1-x) = 1 and, hence, 3 (1996) + (1996) + (1996) + (5…

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Q: 12) The value of f, g,f,and g! are given in the table below live f (x) 3. -3 3 6 -2 -1 2. A) Eind h…

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Q: 4. Intro To Real Analysis

A: Step 1:Solution- Step 2: Step 3: Step 4:

Q: Z is the set of integers, R is the set of real numbers. 1) Functions f, g, h are defined as f: R ->…

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Q: 3. If f, g and h are functions so that the composition makes sense, then the composition of the…

A: Given :Associate property : h∘f∘g=h∘f∘g

Q: .Prove that la + b + c| < |a] + |b| + ]c]

A:

Q: I(¥x (P(x) v Q(x))) ^ (Vx (¬Q(x) v S(x))) ^ (Vx (R(x) → ¬S(x))) ^ (3x ¬P(x))] → 3x ¬R(x)

A: Given: To do: Prove the above statement.

Q: Determine if the following statement is True/False: For every f(n), g(n) such that f(n) ∈ O(g(n)),…

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Q: 2² 1 2²u Show that the equation ax² c² at² u=f(x+ct) + F(x- ct) where fand F are arbitrary…

A: The main objective is to check u=f(x+ct)+F(x-ct) is solution for the given pde.

Q: . What is the expected value and what does it measure? How is it computed for a discrete probability…

A: In the theory of probability, the expected value of a random variable X denoted EX is a…

Q: Simplify the Boolean expression F(x, y, z) = (x+ y) (x +z)

A: F(x,y,z)=(x+y').(x+z) simplify F(x,y,z)=x.x+xz+xy'+zy'

Q: f(x)=x2-1 g(x)=2x+1 prove if the following functions are onto prove if the following functions…

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Q: Let gcd(a, b) = d then which of the following is correct (i) dla (ii) d|b (iii) d[(ax + by) (a) only…

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Q: Væ (L(x) → F(x)) Jx (L(x) ^ ¬C (x)) ... Ja (F(x) ^ ¬C(x)) 2.

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Q: (d) If each fn has fewer than M discontinuities (where M ∈ N is fixed), thenf has fewer than M…

A: To Show: If each fn has fewer than M discontinuities (where M ∈ N is fixed), then f has fewer than M…

Q: 4 This is Discreet math please answer questions with proper formatting for proofs

A: Given that (a)Given two positive integers x and c, if  x+ c &lt; 5, then x5 =x+c5 and (b)given two…

Q: Let P(x) = (x - 1)(x - 2)² (x-3)³. Find the set of r such that x (a) P(x) = 0, (b) P(x) 0.

A: