(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}.

Q: 24. Which is the recursive definition of the set of positive integers that are multiples of 4? * aj…

A: We have to find the correct option which represents the set of positive integers that are multiples…

Q: U = { all real numbers} A = { 10, 11, 12, 13, 14, ...} B = {-3, -2, -1, 0, 1, 2, 3} C = {-1, -2,…

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

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

A:

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

A:

Q: How many triples (x1, 2, 13) of nonnegative integers are there where Xi + x2 + x3< 11. Suggestion.…

A: From the given information. The given inequality is as follows. The suggestion given is to convert…

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)

Q: Tell whether each number is an element of  (a natural number),  (an integer),  (a rational number),…

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

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

A: Natural Numbers: Natural numbers, that embody all positive integers from one to time, square measure…

Q: For any integer ? show that the pair of integers 7? + 9 and 4? + 5 are relatively prime.

A:

Q: How do I prove: If n > 1 is a natural number then there is a prime number p such that p|n.

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

Q: An Example Where the ConversIes False Show that the converse of, "If m and n are even, then m + n is…

A:

Q: A supplier of ballpoint pens guarantees a low defective rate.  Sara receives a shipment of 400 pens…

A: Ww hvae to find values of x ..

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

A: First, we simplify the given expressions. The expression 2/2 simplifies to 1, which is a positive…

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

A: Here we will use the concept of the numbers We know that all set of numbers are subset of the set…

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…

A:

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

A: An integer is a real number which can be represented as a whole number without any fractional…

Q: Let P(n) be the statement n is odd and Q(n) be the statement n is prime. Which of the following…

A:

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…