Show that the set of rational numbers (positive and negative fractions) together with multiplication is not a group. By removing one element, it can be made into a group. Which element? Explain.

Q: We have a group of 10 students that we want to partition into two sub-groups. None of the two…

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Q: Describe how equivalence classes can be used to definethe rational numbers as classes of pairs of…

A: To Describe: How equivalence classes can be used to define the rational numbers as classes of pairs…

Q: The error caused by approximating numbers such as 1/3=0.3333... is called a. Group of answer choices…

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Q: I have 8 different rings that I wear. How many different groups of 3 rings do I have to choose from?

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Q: Pigeonhole Principle Prove that among any 100 integers there always two whose difference is…

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Q: Using the digitd 3, 4, 5, 6, 7, 8, and 9, how many 4-digit numbers can be constructed if the number…

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Q: Prove by mathematical induction

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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: A treasure chest contains 10 rubies and 8 diamonds. In how many ways can a group of six jewels be…

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Q: (a) How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible…

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Q: How many natural numbers that are less or equal to 1000 and that are not multiples of 3, 5, or 7…

A: A number is said to be divisible by other number if on dividing the number  with it given remainder…

Q: Give the transpose of the permutation [2, 5, 1, 6, 3, 4], and find the number of inversions in both…

A: To find- Give the transpose of the permutation 2, 5, 1, 6, 3, 4, and find the number of inversions…

Q: How many 5-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of  digits…

A: It is given that there are six digits 1, 2, 3, 4,5, 6 and 7 and to form five digit number and the…

Q: Suppose we randomly select a subset of integers from the set {1, 2, 3, . .., 60}. How large must the…

A: A subset is the set smaller that the set of which it is a part. A set can be divided into multiple…

Q: 5. If a list of nine integers form a group under multiplication modulo 91, which integer is missing…

A: Using Cayley table, ⊙91 1 9 16 22 53 74 79 81 29 1 1 9 16 22 53 74 79 81 29 9 9 81 53 16…

Q: How many 5-digit even numbers can be formed using the digits 2, 4, 6, 7, 9 if no repetition is…

A: Given:

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: Identify the rational number {5, v7, /16, 3, 3.1458....} O {V7, 3.1458...} O (5, V16, 2} O{V7, V16,…

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Q: How many integers must be negative for the product or three integers to be negative? Explain. Find…

A: Answer is mentioned below

Q: How many phone numbers are possible in the (404) area code of the form ABC-XXXX if: A is restricted…

A: number of ways in which A can be selected (2-9) = 8 ways  number of ways in which B can be selected…

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: A multiset is similar to a set, but can contain an element more than once. How many multisets can we…

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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: How many four​-digit numbers may be formed using elements from the set ​{1, 2, 3, 4, 5, 6, 7​} if…

A:

Q: How many 5- digit numbers can be formed using the digits 0,1,2,3,4,5,6,7,8,9, if repetitions of…

A: Givendigits = 0,1,2,3,4,5,6,7,8,9No.of digits =10

Q: The product of 16 and 7.5 belongs to what group in the Real Number System?

A: Assuming the product means multiplication. (R\{0},*) forms group under multiplication. Also,…

Q: Write the set of natural numbers greater than 16 using the most concise method.

A: We need to write the set of natural numbers greater than 16 using most concise method. We know that…

Q: An event organizer is planning a programme for a group of 20 people who want to embark on a…

A: Note: Thank you for the question. Since multiple subparts are posted, according to our policy, we…

Q: Consider a necklace that is made up of 8 different gems stone such that ruby is always between…

A: As per our guidelines we can answer only one question. please repost other seperately.    7.

Q: 10. If 4,42..a, is an element in a group, what is (4,az..a,) = ?

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Q: Ex: what about Finite in Finite in tersection or of Partition of [a,b]

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Q: How many three​-digit numbers may be formed using elements from the set​{1, 2, 3, 4, 5, 6, 7, 8, 9​}…

A: given:  set ​{1, 2, 3, 4, 5, 6, 7, 8, 9​}   if no element may be used more than once in a number and…

Q: 20 The set [20] contains = = 15504 five-element subsets. How many of them contain more odd elements…

A: There are 15504 five element subsets. The set of 20 numbers contains 10 odd and 10 even numbers. If…

Q: Discuss the important characteristic that a counting problem has to have in order to classify it as…

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

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Q: how many positive intergers less than 1150 are multiples of 8, 5, 3. using the principles of…

A: Floor Function: The floor function , also called the greatest integer function or integer value,…

Q: Explain why it is convenient to write the expression for the number of possible permutations in…

A: It is efficient and time saving, imagine if you want to write 4! in its entire multiplication form…

Q: How many three​-digit numbers may be formed using elements from the set​{1, 2, 3, 4, 5, 6​} if…

A: Given data: Set{1,2,3,4,5,6} To find: Three​-digit numbers  formed using elements from the set​.

Q: Consider the set of rational numbers under the operation of addition. What is the inverse of 9?

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Q: *.elephants live in . .groups X, the

A: The correct options are the following. As the correct statement is "Elephants live in groups.".

Q: Find odd and general

A: Given,       f(x)=x-π3;   0≤x≤π

Q: (2) Explain why the rational numbers are those having periodic representation or with- out infinite…

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Q: 3) Among a group of seven (not necessarily consecutive) integers, how many must be divided by 5 to…

A: This is a problem related to divination rule of the mathematics. Based on the general concept we…

Q: This problem involves the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} and addition modulo 12. Is the…

A: Given :- The set 0,1,2,3,4,5,6,7,8,9,10,11 and addition modulo 12. To Determine :- Is this set a…

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 math teacher will split her class of 15 students into three groups with five students in each…

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Q: Find the least common denominator for the group of fractions. 1 14,  19 84,  2 7,  3 11

A: Consider the given fractions 114,1984,27,311.

Q: Give 5 early mathematicians and their works which they contributed in the development of the study…

A: Topic- geometry

Q: what are infinite subsets?

A: First understand, what is an infinite set?