(3.) Let S be the set of all natural numbers of the form prime. S = { P2 Is 1-2, where p and a { P2= p is prime and S countable? Justify your answer. 2 is prime}.

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Q: Write out explicitly and simplity possible as h= 5 n!

A: ∑n=0n=5 n2n!=?

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A: Since you have asked a question with multiple sub-parts, we will solve the first 3 sub-parts for you…

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A: This is a problem related to set theory. Based on the general formula we will answer the question.…

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Q: For all integers a, b, and c, if a/b and a|c, then a|(5b – 7c). -

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Q: Q1. (a) Let R be the universal set and A = [-7,3], B = (0,8) C = {x:x≤ 10, x € R}. Find of the…

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Q: Let S(n) denote the statement n(n + 1) + (n - 1)(п - 2)(n - 3) (n 4) (n -5) (n - 6) (п -7). 2 his n…

A: (a)

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

Q: Theorem) Let p be a prime number. Then applies p|ab --> p|a or p|b

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Q: Find the smallest positive integer in the given set. (a) {6u + 15v : u, v ∈Z}    (b) {12r + 17s : r,…

A: Given: (a) { 6u+15v:u,v∈Z }(b) { 12r+17s:r,s∈Z }

Q: Question 21 Which of the following expressions is a closed form of the sum of the integers from 92…

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Q: Let b a natural number and q1, q2, r1, r2 integers with 0 ≤ r1 < b and 0 ≤ r2 < b such that q1b + r1…

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Q: (b) If a, b and c are integers such that b| a and b| c, then b | (2a – 3c).

A: We have to proof

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A: This is a theorem of real analysis in which we have to find that there is a p who divides n.

Q: Every none-empty subset of integer numbers contains a least element. صواب ihi

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Q: =) OR Q(6) -) AND Q(3) -) AND Q(6) -) AND Q (5)

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Q: 3) Two points are plotted on the number line below. 十+ -10 -9 -8 -7-6 -5-4 -3-2-1 十十+ 1 3 10 Which…

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Q: For all integers a consider the following statements (A) 6|a - a (B) 6|a + a (C) 6 a – a +1 (D) 6|a…

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Q: • Show that if m divides 3, then m divides 9. (We say a divides b if there exists an integer k such…

A: Let  m divides 3 .  Then there exists an integer k such that 3 = mk. Now, 9 can be written as…

Q: How do I prove: If n is a natural number and d|n prove that d ≤ n.

A: How do I prove: If n is a natural number and d|n prove that d ≤ n.

Q: Determine the set of values of n for which n²-1 n² +1 and are positive integers. 2 2

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Q: Integers a and b are such that (a + 3-5) +a- brS = 51. Find the possible values of a and the…

A: Given integers a and b such that a+352+a-b5=51

Q: (9) √25 N OZ OQ Q OR XRR (h) 1,000 N Z OR (i) ON no R × 300000

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Q: 4. Over the universe of positive integers, define p(n): n is prime and n< 32. q(n): n is a power of…

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Q: ++++ -3 -2 -1 0 1 2 3 4 5 6 7 +++ -3 -2 -1 0 1 2 3 4 5 6 7 -3 -2 -1 0 1 2 3 4 5 6 7 +OTTT→ -3 -2 -1…

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Q: what are the integers of 4 < x < 6

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Q: 6. Solve for x. a) x- 5 = 7 b) 2(x+ 1) = 10 c) 5x – 8 = 2x + 3 d) -5x + 1 = 3x + 2 e) 8 = 4x – 4 f)…

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Q: The set of natural numbers that are less than 7

A: Natural number (N): Natural number which start from 1,2,3,4,5,6,7,8,........

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Q: 1. Assume that t is a particular integer. Use the definition of even, odd, or composite to justify…

A: Even number are those numbers which is divisible by 2. If the unit digit of a number is 0,2,4,6 or 8…