Oa. Every infinite subset of Ris countable.

Q: Find the sup and inf of the following set ∩(1 − 1/n, 2 + 1/n) where n ∈ N

A: The problem is asking us to find the supremum (least upper bound) and infimum (greatest lower bound)…

Q: A class has 26 students. In how many different ways can five students form a group for an​…

A:

Q: How many 4-digit number can be formed out of 1,2,3,4,5,7 and 8 if: a. There is no restriction. b.…

A: Note- Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Decide with a proof that the set Nk is countable or not, where N is the set of natural numbers and k…

A: According to the given information it is required to proof that the set

Q: The set of natural numbers N is .A not bounded above .B bounded above .C bounded below by 0 .D none…

A:

Q: Prove the following statement: For all integers x and y, if x and y are even, then 3x + 5y is even

A:

Q: If  n(A) = 106, n(A ∪ B) = 152, and n(A ∩ B) = 48, find n(B).

A: Introduction: We carry out specific operations in mathematics, such as addition, subtraction,…

Q: Identify the notation used for each of the following concepts. a. k factorial b. The number of…

A: a. k factorial is denoted as k!

Q: Determine if the following sets are closed under multiplication. a. (1,18) b. {2k + 9|keW} c.…

A:

Q: Consider the set A = {0, 1, 2, 3, 4, 5, 6} Find two ways to count the number of subsets of A with an…

A: Let us prove the identity.

Q: Let A be the set of integers that are multiples of 3 between 1 and 15 inclusive and B be the set of…

A: Multiples of 3 between 1 and 15 (inclusive) are {3,6,9,12,15}. Set of even natural numbers up to 20…

Q: How many elements of order 5 are in S7?

A:

Q: Consider the claim "if nm is not divisible by 3, then neither n nor m is divisible by 3." Match each…

A: Note that if a mathematical statement is like, if A then B. The contrapositive statement is, if…

Q: A = all whole numbers except 12 B = all whole numbers except 17 C= {5, 6, 7, 8, 9, ..} %3D a. Is A…

A: Given

Q: #2. If fonel

A:

Q: Set A contains 45 elements, set B contains 52 elements, and 15 elements are common to sets A and B.…

A:

Q: Let O denote the set of odd positive integers. Prove O is countable.

A:

Q: et ZZ be the set of all integers. Let R = {(a, b): a + b is divisible by 3}. a. Show that R is not…

A:

Q: Draw all distinct 4-animals composed of equilateral triangles, squares or regular hexagons that have…

A: The objective is to find all four animals from the given graph.

Q: For all integers a, b, and c, if a | b and a | c then a (b -c).

A:

Q: Prove the following statement: There exists a whole number m such that m² - m - 12 = 0

A: