2. Given that Z denotes the set of all integers and N the set of all natural numbers, indicate the elements of each of the following sets. a. X = {x € Nx 10 and x is divisible by 3} Y = {x € Z\ x is prime, x < %3D b. %3D 30 and x is divisible by 2} c. Z = {x € Z} x² = 4} 3. Let A = {1, 2, 3, 4} and B = {0,1}. Use the set-roster notation to write each of the following sets and indicate %3D the number of elements that are in each set. a. A x B b. B x A C. AX A For items 4 - 5. Give reasons for your answers. 4. Let B = {2, 4, 6, 8, 10} andC = (4,8, 10} and D = {x} x is even}. a. Is D B? b. Is C D? c. Is CS B? d. is B a proper subset of D? 5. a. Is ((-1)2, 12) = (1², (-1)²)? b. Is (V16,) = (4, 12)? c. Is (–2²,0) = (-V16,0)? %3D %3D %3D

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

A:

Q: Find the intersection between the set of all integers bigger than 0 but smaller than 10 and the set…

A:

Q: For the set ?={−3,0,57,−8‾√,2.314520968724609....,14}A={−3,0,57,−8,2.314520968724609....,14}.…

A: Given :A=-3,0,57,-8,2.314520968724609...,14To indentify those that are…

Q: B. Directions: Write the elements of the following sets using the set-builder notation. Set…

A: To write given set into set builder notation.

Q: Find all integers 100 ≤ n ≤ 999 such that the last three digits of n² is same as n.

A: To find: All integers  such that the last three digits of is same as n.

Q: Let the operations * and e be defined on the set of integers. Find each of the following are…

A:

Q: a. Find all pairs of integers such that one is a multiple of 7 and the other is a multiple of 11 and…

A:

Q: test common divisor oint each) 577,27355372

A:

Q: Let a, b, c be three consecutive odd nubmers, with a < b < c. What is the  value of a2−2b2+c2?

A:

Q: I. Identify the type of set (finite, infinite, or empty) as described by the following: 1. A =…

A:

Q: Let S be the set of all real numbers except -1. Define * on S by a*b = a + b + a b. The solution of…

A:

Q: Let a, b and c be integers. Prove that if a does not divide b and a|(b+c), then a does not divide c

A: Let a, b and c be integers.

Q: Assume a, b ER. a+b, a² + b², a³ + b³, and a + b for all integers. Prove that am + bm is an integer…

A: Let us assume that a,b∈ℝ where ℝ is the set of real numbers. It  follows that a,b∈ℤ where ℤ is the…

Q: Graph the following set on a number line and express the set in interval notation. {x\x s -2} -10 -9…

A: Given, {x x ≤ -2}  We have to graph the given set on the number line and express the set in interval…

Q: Which of the following set is empty a. {x: x = x} b. { x : x != x 2 } c. { x : x ! = x } d. {x:…

A: Empty set:            The empty set is the unique set having no elements. and its cardinality is…

Q: 3. Let a₁ = 2, a2 = 1, and for each natural number n > 2, let an 2an-1-an-2. Prove that for all…

A:

Q: 6. Let x and y be integer. Prove the following x + y is odd if and only if x² + y² is odd.

A:

Q: 12. {yly = x² - 1, x = integers}

A: {y/y=x2−1,x∈integer}

Q: Let x and y be non-negative real numbers. Arithmetic mean of x and y is defined by 2, and the…

A: The problem is related to descriptive statistics. Under statistics the arithmetic and geometric mean…

Q: List down the elements of the following sets {x ∈ ℝ : x2 + 5x = -6}

A: Explanation of the answer is as follows

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: d = (a, b, c).

A:

Q: A = {1, 2, 3} b. A = {0, 1, 2, 3} c. A = {-2, -1, 0, 1, 2, 3, …} d. A = {…, - 2, -1, 0, 1, 2, 3}

A:

Q: Denote by mZ the set of all integer multiples of an integer m. More explicitly, тZ 3 {..., -Зт, -…

A:

Q: Let X be a set of integers. How many integers are needed to guarantee that there is a difference…

A: We shall be using the Pigeonhole principle

Q: 1. Find two sets of three consecutive odd integers such that the sum of their squares equals 251.…

A: Assume the first odd integer x. Since the integers are consecutive odd integers, then the next two…

Q: 4. Ax (1-22, 1+22) where A - Z 5. Ax(0, 32, 62) where A - Z 6. A, [5, 10- +] where A = Z' 7. Ax (5+,…

A:

Q: which of the following defines the positive integers divisible by both 3 and 4? Select one: O a. 12…

A: Explanation of the solution is given below...

Q: Find the least element of each of the following sets, if there is one. If there is no least element,…

A: As per our company guidelines we are supposed to solve first three subparts of a question so repost…

Q: Set of months with exactly 30 days. Set of negative integers greater than -8. Set of integer(s) x…

A: Since you have posted multiparts question and we can answer three subparts. So, answered first three…

Q: Use the roster method to describe the elements of the following sets. ([-4,6) n (-3, 11)) nZ =…

A: The given sets,The objective is to describe the elements in the given set by roster form.

Q: This question is split into four groups. Each group has exactly one correct answer. In this…

A: Let's do one by one. The absolute value or modulus of a real number x is  denoted |x|  Namely, |x| =…

Q: For each nonnegative integer n, let Un = (n, -n]. Find U3

A:

Q: Identify the type of set (finite, infinite, or empty) as described by the following: 1. A = {stars…

A: Finite set:-Finite sets are sets having a finite or countable number of elementsInfinite set:-An…