Use Roster Method to represent the sets of natural number that satisfy x + 3 ≤ 7

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: The set of numbers whose decimal representations are neither terminating nor repeating is called the…

A: Explanation:-

Q: h0-60 |--²-1²-₁-²

A:

Q: A company wants to have 4-digit phone extensions with the first digit not being zero. How many…

A:

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

A: Given : F = 4, 5, 6, 7, 8

Q: Determine the number of natural numbers less than 700 that can be written using the digtits 5,6,7,9?

A:

Q: A drawer contains 10 red socks, 10 blue socks, 10 green socks, and 10 yellow socks. What is the…

A: Given : red socks = 10 blue socks = 10 green socks = 10 yellow socks = 10

Q: How many four digit positive integers are there that contain the digit 3 and are divisible by 5?

A: A number is divisible by 5, if the unit digit place contains the number 0 or 5. Let m choices to be…

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: The set of elements in (-, 9) or (-, 12) or in both sets is .

A: The sets are (-∞,9) , (-∞,12)

Q: Suppose a set of 8 numbers are selected from the set: {1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}…

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Q: How many natural numbers are there with a maximum of 7 digits, the sum of which is 31?

A: As per the question we have to find the total number of natural numbers between 0 to 9999999 whose…

Q: 1. The set of counting numbers greater than -1 and less than 9 2. The set of integers satisfying X -…

A: Roster method is to express the set in terms of flower brackets, for example to write the set of…

Q: If a set contains 4 elements then its power set will contain?

A: Here  Set Contains 4 Elements So For n elements  It's Number of powerset =(2^n)

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: Assume that live men and five women are to sit in a row of ten chairs. In how many ways can these…

A:

Q: The exam has 14 questions, and the total number of marks for the exam is 100. In how many ways can…

A: Let us assume that: Pi=The point assigned to the ith question.   Given that:  Each question must…

Q: Maximum number of possible subsets of a set having 4 elements is 18. Select one: True False

A: We have to check

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

A:

Q: The set of numbers {0, 1, 2, 3, 4, ...} is known as the negative integers. whole numbers. positive…

A:

Q: The set of numbers whose decimal representations are neither terminating numbers. repeating is…

A: The set of number whose decimal representations are neitherterminating nor repeating is called the…

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

A:

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: How many subsets does the set  F = {3, 4, 5, 6, 7} have?

A: No. of subsets in a set: The number of subsets in a set containing n elements is given by 2n. No. of…

Q: A company wants to have 7-digit phone extensions with the first digit not being zero. .... How many…

A:

Q: A set contains 7 distinct elements. How many subsets can be formed from the elements of S that…

A: Use combination formula

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 four-digit even numbers are possible if the leftmost digit cannot be zero? repitition is…

A: The question is to find how many 4 digits even numbers are possible if the left most digit cannot be…

Q: The set of elements common to both (-0, 9) and (-∞, 12) is

A:

Q: 11. Discuss briefly using significant word why it might be difficult to describe "a collection of…

A: Given that: 11. A collection of numbers.   NOTE: As per our answering guidelines, we can only answer…

Q: What is the range of all integers greater than 40 and less than 99 that are multiples of 3

A: To find : The range of all integers greater than 40 and less than 99 that are multiples of 3

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: Using the pigeonhole principle How many numbers must be selected from the set {1, 3, 5, 7, 9, 11,…

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Q: How many subsets of a set with 64 elements have more than two elements

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

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Q: How many integers between 1 and 10000(inclusive) are divisible by at one of 9, 10, 11?

A:

Q: How many subsets is obtained from a set with 5 elements?

A: Given n=5

Q: GIve a simple example of the Well Ordering Principle of Integers

A: We have to explain the Well Ordering Principle of Integers using an example.

Q: {xlx is a whole number less than 6} if U is the set of all whole numbers

A:

Q: A set contains fourteen elements. How many subsets can be formed from this​ set?

A: Given that A set contains fourteen elements. To find How many subsets can be formed from this​ set

Q: ) How many,8-distinct/digit numbers can be formed if the numbers áre amultiple of/5 and contain the…

A:

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

A:

Q: The chairs of an auditorium are to be labeled with a letter and a positive integer not exceeding…

A: Given: The chairs of an auditorium are to be labeled with a letter and a positive integer not…

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

A:

Q: Explain Cantor, of way 2. proving the set of algebraic numbers is countable Set.

A: The set of integers is countable, we have this following theorem: So by this theorem, the set of all…

Q: Two sets A and B contains a and belements respectively. If power set of A contains 32 more elements…

A: If a set S contains n number of elements then the number of elements in its power set is 2n here…

Q: Express the set of numbers shown on the number line in set builder notation.

A:

Q: Suppose that all the pages are black and white, but each group of 25 consecutivepages (1-25, 26-50,…

A: To determine the number of ways for the 125 pages to assign to the 5 printers. Given that, the total…

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.