Let N be a set of all positive integers with relation of divisibility. List all immediately predecessors of 27.

Q: Let S be a set of non-negative integers with 80 elements. Show that we can find a subset of S such…

A:

Q: Show that the greater than or equal re lation >) iš a partially order on the Set of integer.

A: Partially Ordered Relation: A relation R on set P is said to be partially ordered if and only if R…

Q: Prove that if n is a +ive integer,

A: Given that, M xddxnf(x);p = (-1)npnF(p) We can prove this by mathematical induction.

Q: Prove that the set of positive integers is equal to the set {1,2,3,...}. (Using Axioms)

A: This is a problem of set theory and cardinality.

Q: Prove or disprove that given a set of 125 integers, one can choose a subset of S of 16 of them so…

A: Given we have set which contains 125 different numbers. When we divide each number in set by 8 we…

Q: Let A be the set of five-digit numbers where only the digits 1, 2 and 3 are included. For example…

A: Given that A is the set of five-digit numbers where only the digits 1, 2 and 3 are included.  So,…

Q: List the set of integers that satisfy the given conditions greater than 12 and less than or equal to…

A: Given conditions are integer should  greater than 12 and less than or equal to 18 integer = x say x…

Q: Find a recursive definition for the set of all integers which are greater than or equal to 15.

A: Sequence is defined as an arranged element that satisfies some definition. Sequences are many types…

Q: Is the set of all of the integers between 12 and 99 finite or infinite?

A: Given : The set of all of the integers between 12 and 99

Q: e the binary operation on Z (set of integers) defined by a * b = 2ab +5 ow that + is commutative.…

A:

Q: Let A be the set of positive integers that are less than or equal to 40 and are multiples of 4 and…

A: Given: Let A be the set of positive integers that are less than or equal to 40 and are multiples of…

Q: 4. Show that for all positive integers n, n! + 1 has a prime divisor greater than n.

A: Let n be an integer such that n>1. All prime divisors of n!+1 must be bigger than n. This is…

Q: Find the smallest positive integer n, пп such that 0 and 0 are 2 coterminal. And give an example

A: Coterminal angles are the angles in the standard position having a common terminal sides.

Q: Determine the identity element of the set N={1,2,3,..} of positive integers with addition.

A:

Q: 4. Show that if n is a positive integer, then Σ {a₁,...,ak}{1,2,...,n} (Here the sum is over all…

A: Given, If n is a positive integer, then we have to show that ∑a1,.....ak⊆1,2,....,n 1a1a2....ak=n

Q: Prove that for any positive integers m and n there are m consecutive positive intege numbers such…

A: As per the question we have to prove that for any positive integers m, n there exist m consecutive…

Q: Prove or disprove that the set Z-{ 0} of nonzero integers is closed with respect to di vision…

A: Consider the given set Z-0 of nonzero integers. The division operation on the set R-0 of non zero…

Q: Discrete

A:

Q: How many positive integers less than 10000 are there which contain at least one 2 or at least one 3…

A: The objective is to evaluate the number of positive integers less that 10000 that contain at least…

Q: n any positive integer n, there exist n consecutive composite integers

A: Given that given any positive integer n, show that there exist n consecutive composite integers.

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

A:

Q: Prove that every nonempty set of negative integers has a largest element.

A:

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

A:

Q: A binary operation * on a set of integers is defined as x*y = x^2 + y^2. Which one of the following…

A:

Q: Let X = {x;} be a set of n positive integers. Show that the sum of the integers of a subset of X is…

A: It is required to show that sum of elements of a subset of described set, X, is divisible by integer…

Q: Determine whether the integers in each of these sets are pairwise relatively prime. a) 21, 34, 55 b)…

A: Given sets of integers are  a) 21, 34, 55 b) 14, 17, 85 determine whether these are relatively prime…

Q: Prove or disprove that the set of all odd integers is closed with respect to addition defined on Z,…

A: Consider a set of odd integers. Prove or disaprove that set of all odd integers is closed under…

Q: Find all positive integers n such that 2" – 1 | 3" – 1. - -

A: Given 2n-1|3n-1 ,  for n∈ℤ+ To find if the statement is true.

Q: Prove that the subset R/Q , the set of all irrational numbers , of R id of second category .

A:

Q: Given 51 distinct positive integers Strictly of Prove two trom to Sum 99 less than 100,

A: Please find the answer in next step

Q: Suppose there is a currency which only uses 3-cent coins and 7-cent coins. Prove that for all…

A:

Q: Prove that there is an integer k for which 2021 = 2k + 1

A: To prove k is an integer  2021 = 2k +1

Q: Let A be a set of integers closed under subtraction. Prove that if A is nonempty, then 0 is in A.

A: Let A be a set of integers closed under subtraction. Prove that if A is nonempty, then 0 is in A.

Q: Let n be an integer. Prove that if 7 divides (n – 2) or 7 divides (n – 5), then 7 divides (n² + 3).

A:

Q: Construct four relatively prime integers a, b, c, d such that no three of them are relatively prime.

A:

Q: Let O denote the set of odd positive integers. Prove O is countable.

A:

Q: Prove that for every positive integer n, there are n consecutive composite integers.

A: This question is related to Descrete Mathematics

Q: Prove that if n, k are positive integers with k | (n +4) and k| (n – 1), then either k = 1 or k = 5.…

A: k | (n+4)  k | (n-1)  => k | {(n+4) - (n-1)} => k | 5

Q: Any two integers are congruent modulo to: even integer odd integer Prime integer not a prime nor…

A: suppose n is a positive integer. Then two integers are said to be congruent modulo n if (a-b) is…

Q: Let S be the set of all (nonnegative) 4-digit integers. How many integers does S contain?

A:

Q: 1) Show that for all positive integers x, x! + 1 has a prime divisor greater than x.

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Let S be the set of all (nonnegative) 4-digit integers. How many integers does S contain? Enter your…

A: Disclaimer: Since you have asked multiple questions we will solve the first question for you. If you…

Q: Prove that 8 divides 9" – 1 whenever n is a natural number. For each natural number n, let P(n) be…

A: To prove that  8 divides 9^n-1 whenever n is a natural

Q: Let the universal set be the set of integers and let A​ = {x​|xsquared ​≤ 5}. Write A using the…

A: Let the universal set be U and the set A is defined as follows.

Q: Let A be a set of 6 integers. Prove that at least two elements of A belong to the same congruence…

A:

Q: Let be a prime number (integer). Show that p2 + 5 cannot be a prime number.

A:

Q: Find all positive integers n such that both n + 2020 and n + 2021 integers. are LVn +1]

A:

Q: Let S be the set of positive integers less than 500. Find the number of integers in S that are…

A:

Q: Consider the infinite set Yof all infinite strings of binary numbers 0,1, for example…

A: We will first assume that Y is countable, then we will use a clever method to construct an unique…

Q: Let A be the set of five-digit numbers where only the digits 1, 2 and 3 are included. For example…

A: