Let A be the set of irrational numbers in [0, 1] and let B be the set of ratinal numbers in [0, 1]. a) Show that m*(B) = 0. b) Show that m*(A) = 1.

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A: Given To prove that a-b is irrational number if a and b are prime number.

Q: Select two positive integers a and b with 5 <  a  ≤  20  and 5  <  b ≤  20.

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Q: Let x be a real number. Which of the following is the same as P(Z x) c) P(Z ≤ -x) d. none of the…

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Q: b) Prove that + ≥ 2, for any nonzero real numbers a and b.

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Q: Show that the first statement is true while the second statement is false. Statement 1: There exist…

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Q: Suppose s and t are distinct natural numbers. Show that lcm(s, t) + lcm(s+1, t+1) > 2st/(sqr(|s −…

A: Given: s and t are distinct natural numbersTo prove: lcm(s, t)+lcm(s+1, t+1)&gt;2sts-t

Q: Let a and b be integers so that (a, b) = 1. Prove that (a + b, a – b) divides 2.

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Q: let a,b,c,d,e and f be different positive integers so that a² - b² = c² - d² = e² - f² = 63. Value a…

A: Given:- a,b,c,d,e and f are different positive integers.  also a2-b2=c2-d2=e2-f2=63. To find :- the…

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: 9) Use the properties of exponents to rewrite the expression in the form kx", where k is a real…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: sing direct proof, prove the following statements: 1. Prove: If x2-4=0, then x = 2 or x = -2. 2. If…

A: follow next step

Q: A) (1 + √₂)² B) (1 -√2)² c)(1+√2)(1+√-2) D)(1+√2)(1-√√2) E)√2² + (√2)² Which of the above…

A: A) 1+22B) 1-22C) 1+21+2D) 1+21-2E) 22+22

Q: 10. Let x be a real number. Prove that at least one of the numbers /2 – x or /2 +x is irrational.

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Q: Use proof by contradiction to show that there is no positive real number x such that (x-2)/x ≥…

A: In an inequality, if a positive number is multiplied then there is no change of sign of inequality.…

Q: Let a, b be nonzero integers with (a, b) = 1. Compute (a + b, a – b).

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Q: a) From the set {-6+2i,  -2.135,  -8, ¾,  √(-16),  √5,   3,  4i,   -1/5} i) List the set of…

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Q: Let Find formulas for the entries of M", where n is a positive integer. Hint: a formula such as 5…

A: Given that the matrixM=16-147-5

Q: Describe the set of real numbers x for which x + 2/ x − 5 > 1

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Q: Suppose that a and b are integers, c b = 3 (mod 19). Find the integer c that a) с%3D 13а (mod 19).…

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