The reciprocal of any positive real number is positive.a. Given any positive real number r, the reciprocal of _______ .b. For any real number r, if r is _______ , then ______________.c. If a real number r _______, ________ then .

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A: As per guidelines we can solve only one question at a time. if you need more answers kindly repost…

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A: see the attachments

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A: (a) Proof of the fact -(a+b)=(-a)+(-b): Since -1 is additive inverse of 1, hence  −1+1=0   (zero in…

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A: It is given that the cube root of any negative real number is negative.

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A: To prove that   the value of an expression (a - 1)(a - 3)(a - 4)(a - 6) + 10 is positive for every a…

Q: all real numbers a

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Q: 5. If x is an integer, then x' 2x. b d a C 6. There exists a real number x such that x'= x . FL

A: we can solve this problem using some basic properties of integers and real number.

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A: A real number x is said to be positive if x>0.

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A: From given statement

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Q: Prove or Disprove the following statements. You may type or hand write your answer. a. For all real…

A: The answer is given as follows:

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Q: Which of the following is NOT true?    A.) If a is in R and a is not equal to 0, then a^2 > 0. B.)…

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A: As per  bartleby guidelines for more than one questions asked only first should be answered. Please…

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A: 11)   All nonzero real numbers have reciprocal.

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A: Given expression: an

Q: 0. If k is a real number, then the real part of 2+i(ki – 3) is А. 2- k. В. -k. С. -1. D. k-3.

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Q: 1. Which of the following represents all real numbers greater than -4 but not more than 8. A) [-4,8)…

A: 1)

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A: To identify the union of the three sets completely

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A: To prove the three parts d, e, f of the problem.

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A: To show the given condition

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A: Let a and b be two real numbers, a, b∈ℝ.

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Q: 4.A.2. Is there an integer that has a remainder of 2 when it is divided by 5 and a remainder of 3…

A: To choose correct option from given question.

Q: 1. Suppose a and b are real numbers. Prove that if 0< a < b then 1/b < 1/a

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Q: 24. The reciprocal of any irrational number is irrational. (The reciprocal of a nonzero real number…

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Q: A b- -1, a-1 n b- 1, a-0 b = 0, a- any real number b = 1, a- 1 b = any real number, a = 1 CCCCC

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Q: 1. The distance from x to 7 is more than 2 2. x is greater than 7 3. x is greater than or equal to 7…

A: As per the questions we can match the answers as below

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.