2. Which are well ordered sets? (a) {x € Z|x > −5} (b) {x = Q|0 ≤ x} n (c) {x € Qx = = ‚n n+1'n=N}

Q: HW6 Proue →1<a = | <aca

A: We have to prove that  For all a &gt; 1, we always have 1 &lt; a &lt; a2 .

Q: Find P (-1.5 < or equal to Z < 0.2) where Z ~ N (0,1)

A: We will use Standard Normal table to find the required probability.

Q: Suppose that f(x) is convex and continuous on an interval I. Show that dif(x1) + ·.+ A„f(xn) + Anf…

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Q: Let n(B) = 5 and n(AUB) = 7. (a) What are the possible values of n(A)? (b) If n(An B) = 0, what are…

A: Let A and B be two sets , then  n(A∪B)=n(A)+n(B)-n(A∩B) . Given that n(B)=5 and n(A∪B)=7 .

Q: 1 - Let A = {x € R: -2-4<x<5+0} B = {x € R: x²(x+y+1)x < 0} Find the set AUB,ANB, A\B, B\A A', B' as…

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Q: {x € Z | x > 0 Ar < 10} n{x € Z | 3y E Z((2 | y) ^ (y | x))}

A: Here first set is all integers between 0 and 10 and second set contains all even integers.

Q: re a deck of 10 cards numbered from 1 to 10. are grey and some are white. rds numbered 1, 2, 3, 5,…

A: The probability of an event is the number of favorable outcomes divided by the total number of…

Q: (2) The floor function is defined as a| = max{m e Z|m < x}. Effectively, the floor function is the…

A:

Q: "/. (e) Evaluate n (c) Evaluate "m(i )

A: We have given

Q: Example 1.73. The intervals (a, b). (-o, bị, ja, oc) are complete.

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Q: (a) Let the interval a, b be divided into n equal sub-intervals such that a = x0 < a1 < x2 < x3…

A: From this general formula we can obtain different integration formulae by putting n=1, 2,3 etc. We…

Q: 4 (i) For each of the following sets state whether it is finite or infinite and in each case justify…

A:

Q: 1. Define the following sets in extension: (i) {x:N|x< 4• 3 * x} (ii) {x,y:N|x < 6^ y< x•x-y} (iii)…

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Q: Which of the following sets are equal? A = {0, 1, 2} B = {xE R| –1<x<3} C = {x E R|-1 <x< 3} D = {x€…

A: first we convert the given roster notation to set or interval notation then compare. ℝ=(-∞,…

Q: Prop (1.23 ≤ x ≤ 1.72) = Prop (-2.50 ≤ x ≤ 0.5) = Prop (x ≥ 3.00)

A: here use normal distribution table

Q: (1) Let f be a function from A to B, {An} a sequence of subsets of A, and {B} a sequence of subsets…

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Q: 1. Let a be a positive real number and n be a natural number. Define S = {x €R: x >0 and x" a?…

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Q: (h) P(1.26 ≤ Z ≤ 2.50) (1) P(1.90 ≤ Z) (1) P(|Z| ≤ 2.50)

A: It is given that the standard normal random variable Z with mean 0 and variance 1.   Note: The…

Q: 2. Let f be the arithmetic function defined by f(n) = (-1)". Compute Z;(2) = f(n) n2 n=1 Hint:…

A: Solution: We will use the following formula Here n0=2

Q: X       P(X=x) 2         0,10 3         0,20 4         0,30 5         0,40   P(3 ≤  X  ≤4 )= ???

A: Given, The probability distribution of X is: X 2 3 4 5 P(X=x) 0.10 0.20 0.30 0.40

Q: {3*} |리 > 3 z – 3 |리 > 3 z – 3 - |z| > 3 z + 3 - Z |리 > 3 z + 3

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Q: Define f: N→ N by f(n) = 2". Find range(f).

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Q: P(- c ≤ Z ≤ c)=0.9399

A: We have given that  P(- c ≤ Z ≤ c)=0.9399 From the given information we have to find the value of c

Q: let a and m be the integers with gcd(a,m)=1, what is the relation between ord m (a) and ord m (-a)

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Q: 5) Given f(x) = V1 -x² , the range is: a) O (-∞; -1] b) O [-1, 1] c) O All real numbers d) O [[0,…

A: The graph is shown below:

Q: If |Z| ≤ 1 and w) ≤ 1, then show that |zw|2s (1z|-|w|)² + (arg z - arg w)²2.

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Q: (a) Lakarkan graf y = e=* dan y = x + 0.5 pada rajah yang sama. Sketch the graphs of y = e¬* and y =…

A: The equation in the form y=f(x) represents a curve in the plane. The point of intersection of the…

Q: Which of the following sets are well-ordered? Justify your answers. (a) A = {r € Q :1> -5} (b) A =…

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you.…

Q: Assume that 0<|x-2|<3. Find the smallest value of a such that |2x-1|<a.

A: Concept: Inequality: All the guidelines you need to be aware of when performing operations on…

Q: Consider the given predicate functions. P(n): "n is a prime number " E(n): "n is an even number" P…

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Q: the suprema and infima of the following sets: (a) {n EN n² < 10}; (b) {mn|m, n€ N}; n (c) {2+1 n €…

A: Since you have posted multipart question and we can answer three subparts. So, answered the first…

Q: (i) Let {I1,I2, I3,· · } be a set of nested closed intervals, that is In+1 C In for all n. Prove…

A: