Is the set closed under addition? If not, explain why. {2, 4, 6, 8, ...}  a) Yes, this set is closed under addition. b) No, 4 + 8 does not belong to the set.

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: 37 How can we use product rule to count number of subsets of a finite set ‘A’?

A: 37 How can we use product rule to count number of subsets of a finite set ‘A’?

Q: Specify the set B in set-builder form by giving a written description of its elements, where…

A: given B={0,1,4,9,16,25} B=0,12,22,32,42,52

Q: Select the collection of sets that forms a partitic

A: Introduction: A set of disjoint subsets of another set. The original set must be equal to the sum of…

Q: Let the Universal Set, S, have 92 elements. A and B are subsets of S. Set A contains 12 elements and…

A:

Q: Which set has higher cardinality: N or Z? Explain with example

A: Cardinality: The cardinality of a set A is the number of elements present in the set A. We denote…

Q: Prove or disprove: For all sets A and B, An(AUB)

A: We have to prove or disprove , for all sets A and B A∩(A∪B)=A.

Q: How many equivalence relations on the set {1, 2, 3}?

A: Given A=1,2,3 we know that a relation is said to be equivalence relation if it is reflexive,…

Q: Determine whether the set spans all of M2. Justify your answer with your work and/or written…

A:

Q: .State all the subsets that apply to /2. Include an explanation supporting why v2 belongs in each…

A: Consider the given expression, 2 the value of the given expression will be, 2=1.4142135624 it can be…

Q: The set of elements common to both set A and set B is called ----------------- the of sets A and B,…

A: Sets are basically a collection of well defined and distinct objects. These objects can be anything,…

Q: The set of numbers in the form , where a and b belong to the set in Exercise 8 and b # 0, is called…

A: Rational numbers are represented in the form of pq where q≠0.

Q: 3. Define two sets, call them A and B, that makes the following statement true; if it is impossible…

A:

Q: Which of these sets are equal: {x, 1, z}, {z, 1, z, x}, {1, x, 1, z}, {1, z, x, 1}?

A: Given sets are x,1,z , z,1,z,x , 1,x,1,z , 1,z,x,1 find out which sets are equal

Q: How may elements are in the set [-2, 2] \N?

A:

Q: Let S be a set containing 700 elements. which is greater, the number of subsets of S having 400…

A: Let S be a set containing 700 elements. We have to justify, Which is greater, the number of subsets…

Q: The set of elements common to both set A and set B is called the______ of sets A and B, and is…

A:

Q: The set of elements common to both set A and set B is called the of sets A and B, and is symbolized…

A: The set of elements common to both set A and set B is called the ________ of sets A and B, and is…

Q: Using induction, prove that a set with n elements has 2" subsets.

A: Let P(n) be the given statements. i.e., P(n): Any set with n elements has 2n subsets.Since any set…

Q: Prove or disprove: For all sets A, B, we must have 24A2(AAB) = 2B.

A: Given, 2A∆2A∆B

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: Explain what is a finite set. Give relevant example along with.

A:

Q: Let the universal set U = {x | x is a positive integer}. Also, let A = {x ∈ U | x is divisible by…

A: Given, U={x | x is a positive integer} The positive integers are  1, 2, 3, ... i.e. the natural…

Q: A set which has ho element is said to be

A: A set with no elements = { }

Q: 2- consider the set of all finite subsets of N, is this set countable or not, prove it?

A: Consider the set of all finite subsets of N, is this set countable or not, to prove it.

Q: Prove: The Cartesian product of countable sets is countable.

A:

Q: Suppose A, B, C are sets. what do you need to show to prove the fllwing definition of subset:…

A: If x is a general element in P ,the given statement implies that each element in P is also in Q…

Q: Describe the set {TER²: doo (r,(0,0)) = 1}.

A: Given: Set x∈R2:d∞(x,(0,0))=1 We have to describe the set.

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

A: Use combination formula

Q: @ (А-В)- С 3 (А - С) - В

A: Introduction :

Q: 4. Explain how bijection can be used to define the cardinality of an infinite set. Using that idea,…

A:

Q: (BUA)'= Give a 3 element subset of set B.

A: Given : U = 1,2,3,4,5,6,7,8,a,b,cA = 2,4,6,8B = 1,2,3,4,a,bC = 4,8,a,c

Q: how many subsetsof one or more elemets can be formed from a set containing 12 elements?

A: Use concept of power set

Q: Identify the set shown below as finite or infinite, {10, 11, 12, ..., 40} ..... OInfinite O Finite

A:

Q: Suppose we modify the construction of the Cantor set by starting with the open interval (0, 1) and…

A:

Q: Describe the set {TER²: doo (r,(0, 0)) = 1}.

A: To Describe: the set {x∈ℝ2: d∞(x,(0,0))=1}.

Q: Prove that empty set is subset of all sets: φ ⊆ A     Please help me figure this question out.

A:

Q: Write down the non-empty proper subset of the set {a,b,c}. Make sure to use correct notation…

A: Consider the given set A = {a, b, c}. A proper subset of a set A is a subset of A that is not equal…

Q: 3. Find the number of subsets for set containing 3 elements.

A: Given set  containing 3 element

Q: Let U be the universal set of all the letters in the English alphabet. What is the complement of the…

A:

Q: Set A contains 6 elements, set B contains 12 elements, and 4 elements are common to sets A and B.…

A: Set A contains 6 elements, set B contains 12 elements, and 4 elements are common to sets A and B.…

Q: Please prove the statement below: For all sets X, Y, and Z subsets of a universal set U (X -- Y) ∩…

A:

Q: What is the intersection of (a) the sets {0, 1, 3} and {1, 2, 3}; (b) the set of girls in this class…

A: Given information Part (A):- The intersection of sets {0, 1, 3} and {1, 2, 3}. Take A=0, 1, 3,…

Q: Let A and B be infinite sets that are countable. Do A and B necessarily have the same cardinality as…

A: Given question is Let A and B be infinite sets that are countable. Do A and B necessarily have the…

Q: 2. Write the set of positive odd integers in set-builder notation.

A:

Q: {(x,a), (x,b), (x,c), (y,a), (y,b),(y,c)} is the Cartesian product AXB of two sets given as

A: Given,          x,a,x,b,x,c,y,a,y,b,y,c is the Cartesian product of A×B.

Q: Let the Universal Set, $, have 92 elements. A and B are subsets of S. Set A contains 27 elements and…

A: Given information nS=92 nA=27 nB=57 nA∩B=24 We have to find the number of elements are in neither in…

Q: what are infinite subsets?

A: First understand, what is an infinite set?

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”.