f a is not algebraic, then it is called transcendental. Let A denote the set of algebraic numbers and T be he set of transcendental numbers. 1. Show that A is countable. 2. Show that T is uncountable.

Q: C and D are sets of real numbers defined as follows. C={z | z>1} D={z |z>8} Write CUD and Cn D using…

A: Given are the sets as follows: C=z|z≥1D=z|z>8. Here z∈ℝ. It is required to find C∪D and C∩D. The…

Q: 2. Decide whether each of the following sets are finite, denumerable or uncountable. Explain each of…

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Q: Let the universal set be the set R of all real numbers and let A={x eR|-2<x<2} and B = {xe IR|-3<x <…

A:

Q: (2) If h is defined by h(x) = |x| + 2, (a) What is the range of h if the domain of h is the interval…

A: 2) We will modify the domain to determine the set of occuring of |x| + 2, which will be the range.

Q: Suppose that the functions s and t are defined for all real numbers x as follows. s (x) = 2x? t (x)…

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Q: Assume that a and b are real numbers such that a <b. Prove that the interval (a,b) is an open set.…

A: Given that a and b are real numbers and a&lt;b. Prove that (a,b) is an open set

Q: Let V; = for each positive integer i. Find each of the following. (Enter your answers using interval…

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Q: Let V, = xER for each positive integer i. Find each of the following. (Enter your answers using…

A: As per guidelines, we will solve only first three parts. If want want another part to be solved,…

Q: If ? isdefined by h(x)=|x|+2, (a) What is the range of ? if the domain of ? is the interval [−8,2)?…

A: For the given question ? is just a representation for h .To identify the ranges of particular…

Q: B and C are sets of real numbers defined as follows. B={w | w>1} C={w|w>6} Write B U C and B N C…

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Q: B and C are sets of real numbers defined as follows. B= {z | z>3} C= {z | z<9} Write B n C and BU C…

A: topic - relation and sets

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) =x s(x) = 3x²…

A: givenr(x)=x3s(x)=3x2(s-r)(x)=s(x)-r(x)=3x2-x3      answer(s.r)(x)=s(x)r(x)=3x2.x3=3x5     answer

Q: II. Let U = R I = {x € R|x° – 14x³ + 45x = ( J = {x €R|x° 2}. Find the following. All infinite sets…

A: We have I={x∈ℝ|x5-14x3+45x=0} Solve for x in  x5-14x3+45x=0, We get I={-3,-5,0,5,3}.

Q: F and H are sets of real numbers defined as follows. F={y|y>1} H={y|y<8} Write FU H and F N H using…

A: NOTE: Refresh your page if you can't see any equations. . given inequalities:   use the number line…

Q: R.1. Use the Schröder-Bernstein Theorem to prove that the intervals [0, 1) and (1, ∞) on the real…

A: The trigonometric tangent function sprang to mind first, and a strategic linear transformation of…

Q: If ? is defined by h(x) = |x| + 2, (a) What is the range of ? if the domain of ? is the interval…

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Q: (a) Let S be a set of real numbers with the property that if x1, x2 € S, then the midpoint (x1 + x2)…

A: a) Let S be a set of real numbers with the property that if x1,x2∈S, then the midpoint 12x1+x2 also…

Q: 2. For each of the following sets, determine whether each of these statements is true or false.…

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Q: Let A and B be nonempty sets of real numbers. If sup A exists then: O a. sup (A U B) exists if…

A: a)If sup A and sup B exists then          supA∪B=max{sup A,sup B} So supA∪B exists. First option is…

Q: Let the universal set be the set R of all real numbers and let A={xe R|-2<x<2} and B= {x e IR |-3<x…

A:

Q: Suppose A is a set with n elements and B is a set with m elements. (a) How many ordered pairs (a, b)…

A: By bartelby guidelines I can only answer the first three sub questions.

Q: Let R, = = 1, 1 + for each positive integer i. (Enter your answers using interval notation.) (a) 7…

A:

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) =x+6 s…

A: Given : rx = x + 6sx = 4x + 4

Q: (5) Show that for any real number x and a subset A of R, exactly one of the following holds: (a) x…

A: To prove: If x is any real number and any subset A of ℝ, then either x is an interior point of A or…

Q: Assume the following three statements are true. p: For all real numbers x and y, if xy is…

A: We are given that statements p,  q and r are true. We need to prove that 2a-1 or a2+3 is…

Q: Define sets A and B as follows: A = {n €Z|n= 8r - 3 for some integer r} and B = {m €Z|m = 4s + 1 for…

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Q: Let the domain be the set of all integers. Determine if the following predicate statement is true or…

A: We need to determine if the given statement id True or False.  ∀x∃y (x-y=0) means for all x there…

Q: Suppose that x is a real number and that UCR. Prove that the following two conditions are…

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Q: Let R+ = {x € R|x>0} be the set of positive real numbers. Let A = [a,b), a,beRb +00, be an (right…

A:

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) = 6x s (x) =…

A: Given  rx=6xs(x)=2x+3 where the expression for r+sx,  r-sx  and  r·s2 is to be evaluated.

Q: Let P denote the set of integers strictly greater than 1. For i> 2, define X;= {ik|k e P}. Describe…

A: Given P=n|n∈ℕ,n&gt;1 Then,  Xi=ik|k∈P=multiples of i Claim: ∪i=2∞Xi=Set of Composite numebrs Proof:…

Q: Recall that a set B is dense in R if an element of B can befound between any two real numbers a &lt;…

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Q: Suppose that the functions r and s are defined for all real numbers x as follows. r (x) = 3x s(x) =…

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Q: 2. Classify each of the following sets as open, closed, neither, or both. Then, find the closure. a)…

A: classify the given sets are open and closed.

Q: and D are sets of real numbers defined as follows. C= {z |zs3} D = {z |z<6} ite CUD and Cn D using…

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Q: Consider the set of mathematical formulas F, Inductively defined as the smallest set that meets the…

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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: 17. Let a and b be real numbers with a 0, the number x belongs to the open interval (a – €, b + €).…

A: Given that a and b be real numbers with a&lt;b, and x be a real number. Let for each ε&gt;0, the…

Q: F and H are sets of real numbers defined as follows. F={v|v<4} H={vI vs아} Write Fn H and FUH using…

A: Given, F={v|v&lt;4}H={v|v≤6}

Q: a. Let S= Z (the set of integers). Define t < s by s – t is non-negative. Prove or disprove that…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Show that for any real number x and a subset A of R, exactly one of the following holds: (a) x is an…

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Q: Consider the set Q = Z × (Z 10), and the relation fupon QDefined as: (a, b) ↑ (c, d) + a•d=b•c…

A: We are given the set Q=Z×(Z 10), and the relation ↑ upon Q defined as:…

Q: Let A, B be sets of real numbers. We will say that B is dense in A if for any sE A and for any real…

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Q: Let the universal set be the set R of all real numbers and let A={xeR|-2<x<2} and B= {xeR|-3<x<1}.…

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Q: a) Let the universal set be the real numbers R and let A {x €R|2< x <7} and B = {x ER | 1 < x < 5}.…

A: First we find intersection then find compliment

Q: (2) If h is defined by h(x) = |x| + 2, (a) What is the range of h if the domain of h is the interval…

A: Range of modules function

Q: { // - // | m, n {N} write the infimum, mini mum, maximum and supremum of each of the ff. sets…

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Q: Define the real numbers R to be the set of all cuts in Q.

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Q: E and F are sets of real numbers defined as follows. E = {w | w<3} EUF=- F={w |w<6} En F=E 3,65…

A: