Is {1, 3, 5} a subset of the set of odd integers?

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

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Q: Suppose that the number of subsets with k elements, made out of a set of n elements is called by the…

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Q: b) Suppose we randomly select a subset of integers from the set {18, 19, 20, 21, 22, 23, . ,717}.…

A: This is an interesting question but before the solution i want to tell about the subset of a set "…

Q: How many subsets does the set  F = {4, 5, 6, 7, 8}  have?

A: Given : F = 4, 5, 6, 7, 8

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: How may elements are in the set [-2, 2] \N?

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Q: In a set of 2 positive integers, how many ways it can be chosen in less than 50? 1.

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Q: of the first 150 positive integers?

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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: Determine the number of permutations of the set {1 ,2 ,..., 14} in which exactly 7 integers are in…

A: Solution-:

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: Show that the set {2/3,1/3,2/9,1/6...} is countable

A: Given set of numbers{2/3, 1/3, 2/9, 1/6...}. Here, this set of rational numbers will be proved as…

Q: How many triples of integers from 2 through 16 can be formed in which the integers are in increasing…

A: Any triple of integers (i, j, k) with 2 ≤ i ≤ j ≤ k ≤ 16 can berepresented as a string of 15 – 1…

Q: How many numbers must be selected from the set {1, 2, 3, 4, 5, 6} to guarantee that at least one…

A: To find  How many numbers must be selected from the set {1, 2, 3, 4, 5, 6} toguarantee that at least…

Q: In how many distinct ways can the digits in the number 1,238,229,168 be arranged?

A: We have to find in how many ways the number  1,238,229,168 can be arranged.

Q: How many pairs of two distinct integers chosen from the set {1, 2, 3,..., 101} have a sum that is…

A: Since you have posted multiple questions and we can answer one question. So answer provided for the…

Q: Show that if seven integers are selected from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, there must be…

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Q: How many pairs of integers (a,b) exists such that the product of a,b and HCF of (a,b) is 1080??

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

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Q: determine the number of computer can randomly generate one such integers from 1 through or more 12.…

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Q: Show that if any 14 numbers are selected from the set S = {1,2, 3, ..., 25}, %3D there are at least…

A: Given statement is If any 14 numbers are selected from the set S = {1,2,3,...,25}, there are at…

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: Show that given any set of 5 natural numbers, there are 3 numbers whose sum is divisible by 3.

A: Let q∈N. Note that, for every q there exists some x∈N and some v∈0,1,2 such that q=3x+v. Now, let…

Q: How many integers in the set {1,2,3,4, ..., 200} is divisible by at least one of the primes 2, 5 and…

A: Just use inclusion-exclusion principle for three sets.

Q: How many subsets of set S = {1, 2, 3, 4, 6} do not contain odd numbers? Use bijection to solve this…

A: Solution S={1,2,3,4,6}

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: Let i be a positive integer and A; = {...,i – 6, i – 4, i – 2, i, i + 2, i + 4, i + 6, ... }. Then…

A: Just substitute i equal to 1,2,3,... And you'll observe a pattern.

Q: 2. Show that if a]b then a'|b² for all integers a and b (Symbols V, 3, A, V, V,A,→,-)

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Q: What is the set N of all natural numbers?

A: Set of all integers: ℤ={.......,-3,-2,-1,0,1,2,3.......} Set of all positive integers…

Q: How many pairs of two distinct integers chosen from the set {1, 2, 3, 101} have a sum that is even?

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Q: Show that the set {2/3, 1/3, 2/9, 1/6,...} is countable

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Q: Show that if n is an odd integer then []

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Q: 4.The set of integers from 1 to 10 that is divisible by 3.

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Q: Let i be a positive integer and A, = (.-7.1-5,1-3,1-1,1+1.1+ 3,1 + 5,). Then N A ONone of these O…

A: The set is:-

Q: How many numbers must be selected from the set {1, 2, 3, 4, 5, 6, 7, 8} to guarantee that at least…

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

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Q: Use a Venn diagram to illustrate the subset of odd integers in the set of all positive integers not…

A: Let us denote the set of positive integers not exceeding 10 by 'X' and the elements can be listed as…

Q: How many elements are in the set {0, {0}}?

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Q: Show that the set of odd numbers is countable.

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Q: How many subsets are there of the set N = {1, 44, 65, 11, 39, 53, 26}?

A: Given,          The set is N=1, 44, 65, 11, 39, 53, 26We know that,          The number of subsets…

Q: How many integers from 1 to 500 are divisible by at least one of  the numbers 3, 4, 5?

A: Given :  Integers from 1 to 500 Total numbers  = 500 So to calculate the number of divisors, we will…

Q: What is the intersection of (a) the sets {0, 1, 3} and {1, 2, 3}; (b) the set of girls in this class…

A: Given information Part (A):- The intersection of sets {0, 1, 3} and {1, 2, 3}. Take A=0, 1, 3,…

Q: How many distinct proper subsets are there of the set N = {4, 49, 63, 12, 36, 55}?

A: A proper subset is subset which is not the whole set itself.    There are 2n subsets of a set where…

Q: A natural number greater than 1 that is divisible by a number other than itself and 1 is called a/an…

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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: Assume that A = { 1, 3, 5, 8, 9}and that U = set of natural numbers less than 11. Find A'. * O {2,…

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