What is the set of O of odd positive integers less than 10?

Q: 3. How many 4-digit positive integers are there that are even or contain no O's?

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Q: What is the set M of positive integers less than 100?

A: Given statement is set consist all those positive integers less then 100. Collection of all these…

Q: are there any even numbers greater than 2 which are prime? why or why not?

A: We will find the solution in the following step

Q: Prove for any positive integer n, n=floor(n/2) + ceiling(n/2)

A: Given,          n is a positive integer.     To show-                 n=floor(n/2) + ceiling(n/2)…

Q: What is the converse of: an integer has divisors other than 1 and itself, if an integer is…

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Q: What is the set Z+ of all positive integers?

A: Set of integers are represented as: ℤ={.....,-3,-2,-1,0,1,2,3.........} Set of natural numbers:…

Q: 1. Show that subtraction is not associative for the set of integers.

A: Definition :Let "." be a binary operation and A is a setThen "." is said to be associative for A if…

Q: If ten integers are chosen from between 0 and 21 exclusive, must at least one of them be even?…

A: Pigeon hole principle states that if n objects are put in to m containers with n>m then at least…

Q: How many positive integers less than 850 are multiples of 8, 3, or 5? Use the Principle of…

A: Using the Principle of inclusion/Exclusion, the formula for A∪B∪C can be written as:…

Q: The diagram below shows ten circles joined by five lines with three circles Place all the…

A: Requirements: Numbers should range from 1 to 10.   Every line has three circles.   3. The amount for…

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: If seven integers are chosen from between 1 and 12 inclusive, must at least one of them be odd? Why?

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Q: List the set of integers that satisfy the given conditions; a positive multiple of 5 and not a…

A: The given condition is that element of the set should be positive multiple of 5 and not a multiple…

Q: a) How many 3-digit positive integers are there with odd digits?

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Q: Which positive integers less than 20 are relatively prime to 20?

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Q: The sum of all positive integers less than 300 which are divisible by 3.

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Q: Set C is the set of positive two-digit even numbers less than 56 that are divisible by 5.

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Q: Discrete

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

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Q: Show that for all integers n:  ceil(n) = -floor(-n)

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Q: Give two reasons why the set of odd integers under addition is not agroup.

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Q: How many positive integers between 50 and 100 a) are divisible by 7? Which integers are these? b)…

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Q: Let A be the set of all positive integers whose last two digits form a number that is evenly…

A: We have the given condition as   Let us consider A be the set of all positive integers whose last…

Q: 2. Use a Venn diagram to illustrate the subset of odd integers in the set of all positive integers…

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Q: Show that, selecting 91 positive integers guarantees that there are at least 10 integers with the…

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Q: Is the set O of all odd counting numbers (1, 3, 5… ) closed for multiplication? Why or why not?

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Q: 5. Give a recursive definition of the set of positive integers that are multiples of 5.

A: Solution

Q: Write “the set of all natural numbers N less than 9” intwo different ways.

A: To write “the set of all natural numbers N less than 9” in two different ways.

Q: show that every integer greater than 11 is the sum of two composite integers

A: We need to prove that  every integer greater than 11 is the sum of two composite integers.

Q: 3. If а, 1000". Find N E I, the set of positive integers, such that an+1 N). n!

A: Given an=1000nn!. We have to find the N∈I such that an+1<an, n>N. For n=1 a1=100011! For n=2…

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

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Q: 12 belongs to the set of natural numbers

A: The natural numbers (i.e. counting numbers) are numbers which are used for counting and ordering.…

Q: Find how many positive integers with exactly four decimal digits, that is, positive integers between…

A: The positive integers between 1000 and 9999 is calculated as follows.

Q: How many positive integers not exceeding 3000 are divisible by exactly two of 4, 10, 12? (Steps…

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

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Q: The sum of all positive integers less than 400 which are divisible by 5.

A: Positive integers less than 400 which are divisible by 5 are⇒n=79 5,10,15,20,...,395 The above…

Q: Use the roster method to write the set of natural numbers less. Than 12

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Q: If n is an integer greater than 2, then for all integers m, n does not divide m or n + m # nm.

A: c Given n∈Zand n>2. We have to prove that for all m∈Z, n/m or n+m/nm. Suppose n/m and…

Q: Suppose 26 cars start at a car race. In how many ways can the top 3 cars finish the race? ..... The…

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Q: Choose two distinct integers, x and y, between 0 and 9. Derive the number of 9- digit integers that…

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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: How many integers from 1 to 99,999 contain exactly two consecutive 1s?

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Q: that the set of negative integers divisible by 3 is countable

A: Set of negetivee integers divisible by 3 isS=-3n, n∈ℕf: ℕ→S   defined asf(n) = -3n,To check…

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

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Q: Suppose that n students take a quiz and their scores sum to 150. What is the smallest number n to…

A: Pigeonhole Principle: The pigeonhole principle states that if n items are put into m containers with…

Q: A restaurant sell features a burrito bar in which a customergets to choose one of 2 different kinds…

A: As per bartleby guidelines only one question is answered please upload the other one separately…

Q: How many corresponding integers are made up of 1443 digits taken from (1-2-3-4-5-6) provided that no…

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Q: What is the set Z of all integers?

A: The set of all integers is, ℤ=........, -4, -3, -2, -1, 0, 1, 2, 3, 4, ........