A. Is the set of all positive integers closed for subtraction? Is the set of all positive integers closed for multiplication? Explain your answer. Subtraction: Multiplication: B. If a bug crawls from the lower left corner of a wall to the upper right corner diagonally, how much shorter is its trip compared to crawling horizontally from the lower left corner of the wall to the lower right corner and then straight up to the upper right corner? Assume the wall is a 30 feet wide and 9 feet tall, and give your answer to the nearest foot

Q: Determine whether it is possible to express 1 as a liner combination of 1 = m· 44 + n· 91 ,. for…

A:

Q: It is possible to find two integers whose multiplication is -4 and whose summation is 0. Select one:…

A: Sum of 2 and -2 is 0 and multiplication of 2 and -2 is -4. So, given statement is true. Sum of 3 and…

Q: Find the greatest natural number n such that n + 10 divides nº + 100.

A:

Q: In a colored-counter model, an integer is represented by a set of counters--red and black discs are…

A: Black counters represents = positive integer  Red counters represents = negative integer

Q: (a) Find the number of integers between 32 and 395 that are divisible by 6. (b) Find their sum.

A: (a) The first term of the integers between 32 and 395 is a1=36 which are divisible by 6   and the…

Q: n(nº +5) is divisible by 6, for each integer n 0.

A:

Q: Can you use mathematical induction to show that 4 divides 32x + 7 First define the predicate P(x)

A: Yes we can use mathematical induction for Natural number x.

Q: R.1. Show that among 14 distinct integers, there must be two that have the same remainder when…

A: In order to prove this statement pigeonhole principle has to be applied. According to pigeonhole…

Q: 4.2: Subtracting Integers using Chips Vocabulary and symbols – write out what the following mean:…

A: Zero pair: The pair which consist of one positive valued and one negative valued chip hence the…

Q: Show that if n is any integer, then 3 divides n3 − n

A: To prove:  if n is any integer, then 3 divides n3 − n. Concept used: Here we shall use the identity:…

Q: Identify the property of integers being illustrated in 1[2( 4)] = (1 • 2)(¯ 4).

A:

Q: O Given any integers a, b, and c, if a - b is odd and b- c is even, what can you say about the…

A: The parity of a-c will be odd. We will prove this by using the fact that a-b is odd and b-c is even.

Q: Find the product of all positive integers from n down through 1 for n = 5.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: How many numbers between 1 and 10000 have the digits 1,3, and 5 such that each digit appears exactly…

A: Here Numbers between 1 and 10,000 have digits 1,3,5 and each appears exactly once only

Q: 3.a) Evaluate: 100 b.) let n a positive integer and r# 1 be a positive be real number. Evalyate:

A: Let's find.

Q: (b) Determine whether 6|(n³-n), for each integer n ≥ 0.

A: 13) b We prove that n3-n is divisible by 6 by using mathematical induction   Basis step: For n=0…

Q: (a) How many positive integers divide 10!.

A: Since  you have posted a multiple  question according to guildlines I will solve first   question…

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

A:

Q: Any n consecutive integers will include a number that is divisible by n.

A:

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

A:

Q: (b) Find the sum of the first 110 positive odd integers.

A: Our Aim is to find the sum of the first 110 positive odd integers.

Q: Are the integers closed under division? Choose the correct answer below. Yes O No

A: Solution :-

Q: Find the total number of integers 'n' such that 2 ≤ n ≤ 2000 and H.C.F. of n and 36 is 1.

A:

Q: (b) An integer is divisible by 3 if and only if the sum of its digits is divisible by 3.

A:

Q: se indirect proof to show that, "If n is an integer and 3n + 2 is even, then n is even

A: Let us solve the classical algebra problem in the next step.

Q: Are the natural numbers closed under addition? Choose the correct answer below. O Yes O No

A:

Q: (a) Suppose that there are k distinct positive integers that divide an odd positive integer n.…

A:

Q: 2. The number of ways of arrangingr objects from n objects in order is called the number of . of n…

A: Given: The number of ways of arranging r objects from n objects in order is called thenumber of…

Q: Are the integers closed under division? Choose the correct answer below. O Yes No

A:

Q: Find integers μ and λ such that λ48 + μ57 = 3.

A: Find integers μ and λ such that λ48 + μ57 = 3.

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: nd the distance between G and H on the number line below. G ++ -12 -11 -10 -9 -8 -7 -6 + 5 6 7 8 9…

A:

Q: If m is a positive integer, does 6 divide (2m)(m+2)(3m+3)? True False

A: Here, the given number is: (2m)(m+2)(3m+3)=2(m(m+2))3(m+1)=6m(m+1)(m+2) because multiplication is…

Q: Suppose that 56 % of students play football, 53 % of students play cricket, and 12 % of students…

A: Let F=students play footballC=students play cricketGiven,P(F)=0.56P(C)=0.53P(F¯∩C¯)=0.12

Q: Suppose that one selects some subset of integers from the set {1, 2, ., 47). What is the smallest…

A:

Q: 6. What is the sum of all 100 positive odd integers starting with 1? Apply your common sense if it…

A: Given n=100

Q: Show that 3-4" + 51 is divisible by 3 and 9 for all positive integers n.

A:

Q: Al. a. Find an integer that leaves a remainder of 2 when divided by either 3 or 5, but that is…

A:

Q: Are the integers closed under multiplication? Choose the correct answer below. O No O Yes

A:

Q: Suppose a deep sea diver dives from the surface to 500 feet below the surface. He then dives down 25…

A:

Q: is ​{x | x is a fraction between 71 and 72​} finite or infinite

A: We will solve the problem. There are infinite real numbers between any two natural numbers. These…

Q: Find the sum of the integers from −20 to 256.

A: It is required to calculate the sum of integers from -20 to 256 that is:

Q: How many zeros are there at the end of 1001?

A: This question is related to Number Theory

Q: Is it true that for any odd n the number 2" +1 is divisible by 3? Prove your answer.

A: We prove this by using PMI(Principle of Mathematical induction)

Q: Find the sum of all natural numbers n such that 2021-n/99 is a natural number ?

A:

Q: 1. Show that the set of integers S = {a² + b2 : a, b € Z} that can be respresented as the sum of two…

A: See the details below.

Q: How many zeros does 4000! end in? Justify your answer, show your work

A: It is required to find the number of zeros at the end of 4000!. To calculate the number of zeroes in…

Q: M is the set of integers that are greater than -1 and less than 4.

A: M is the set of integers

Q: a) Find the number of positive integers not exceeding 120 that are divisible by 3 or 4. 1 0 01 0 0 0…

A: As per our guides lines I answered only 1st part

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”.