Let, x belongs to positive integers. A, B and C are the sets expressed with the following set buile notations. A = {x |x is prime number not exceeding 15} B = {x|x is positive odd integers not exceeding 15} C = {x |x is positive integers not exceeding 15 and divided by both 2 and 3}

Q: Let J={1,2,3,…}, the set of counting numbers and let R be the set of real numbers. Is R-J countable?…

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Q: Let "xy" denote "x does not divide y." Prove by any method. Let a and b be integers. If 3 ab, then…

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Q: Find the intersection between the set of all integers bigger than 0 but smaller than 10 and the set…

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Q: List the first four elements of the set { x | x = 4k + 1, and k is a natural number}  (List each…

A: Given set { x | x = 4k + 1, and k is a natural number} = {4×1+1, 4×2+1, 4×3+1, 4×4+1, ... } = {5, 9,…

Q: For the set ?={−3,0,57,−8‾√,2.314520968724609....,14}A={−3,0,57,−8,2.314520968724609....,14}.…

A: Given :A=-3,0,57,-8,2.314520968724609...,14To indentify those that are…

Q: Show that 2N, the collection of all sets of natural numbers, is uncountable.

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Q: Denote the set using the listing method {x| x is reciprocal of a positive odd number

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A: We have to find a set of four integers such that their order and the the order of their absolute…

Q: What is the largest number x such that x<200 and x has exactly 4 factors?

A: Factors:    Number that are multiplied together to get a product                              Factor…

Q: 2. Which of the following sets does not contain any inrational numbers? a. (-5.12, 1, 30) c.(, VT00,…

A: The sets are, -5.12, π, 30 92, 100, 5.123 80, 100, 6.56 5.123....,12, -65

Q: Define the following sets: A=(1,3,7,9,10) 6-(2.5.7.8.9.10) C = (0,1.3.10) D=(2,4,6,8,10) E=xxis a…

A: Natural numbers do not include negative numbers.

Q: For any integers a and b, a + b ≥ 15 implies that a ≥ 8 or b ≥ 8.

A: Let a+b≥15, where a,b are integers.   Case 1: b&lt;8 Then: b&lt;8⇒-b&gt;-8⇒15-b&gt;15-8⇒a≥15-b&gt;7…

Q: For each pair of integers r and s below, Find the greatest common divisor d. Then, find m, n, such…

A: To determine the greatest common divisor, d and then to find m and n such that d = mr + ns. (a) r=32…