44 Answered Questions for the topic Set Theory

Set Theory Calculus Functions


Set Theory - Functions & Set Duplicates

Hey there! I'm really looking to understand a property of set theory. I've built a function PS() that takes in a set and returns a set. However, the output set may have duplicates. The definition... more

Discreete math functions

Let A, B be sets and f : A → B a function between them. Let also C, D ⊆ A and E, F ⊆ B be subsets. Prove the following. 1. f(C ∩ D) ⊆ f(C) ∩ f(D) 2. f−1(E ∩ F) = f−1(E) ∩ f−1(F)3. f−1(C) \... more
Set Theory Math Algebra Sets


What is A' ∩ (B-C)?

Let A = {1,2,3,6,7} B= {2,4,5,7} and C = {2,4,6} and U = {1,2,3,4,5,6,7,8}a. {6}b. {5}c. {}d. none of theseI have answered B. {5} am I correct?

Discreete math question

Let R be the relation Z defined by aRb if and only if a^2=b^2. Show that R is an equivalence relation on Z and determine its distinct equivalence classes.


Venn diagram to expression.

How do I make an expression out of this Venn diagram. I know that the intersection between A and B can be described as A ∩ B. But how do I include the universal set. That is, all the gray that is... more


Is this website correct about p(∅)?

I am learning about power sets.I know that p(∅) = {∅} or {{}}.That is a little confusing to me, so I used an online calculator (https://www.mathsisfun.com/sets/power-set-maker.html). After putting... more


Set Theory and Lists

If A = {b, {b}, ∅} how would we use list notation to write {B: B ⊆ A and B ≠ ∅} If you could explain what I need to do to solve this that would be much appreciated.
Set Theory Calculus


Set Theory Question

Prove f(a1∩f^-1(b2)=f(a1)∩b2
Set Theory Algebra 2 Inequalities


Problem on two variable polynomial inequalities (Probably a diophantine inequality !!)

Consider the sets defined by the real solutions of the inequalities :A = { ( x , y ) : x2 + y4 ≤ 1} B = { ( x , y ) : x4 + y6 ≤ 1}Then... more


What are ways to use the palindromic property of a palindromic scale?

A palindromic scale, as I've seen it described on a number of music theory websites, is defined as one whose sequence of intervals is the same when ascending and descending. For instance: D Dorian... more
Set Theory


About continuum hypothesis

Sir why continuum hypothesis isn't falsifiable. It states that "There is no set whose cardinality is strictly between that of the integers and the real numbers"; so can't we make a set which... more
Set Theory


State the number of elements in the set, if possible

A={×:×∈Ζ, -6<×≤4}


Bernard's Cars Problem (algebra) - Please help me with this problem.

Bernard, who is a genius and very wealthy, owns one thousand cars, each of which is numbered with a different natural number from 1 to 1000. He invites 1000 people to a party, and he makes each... more
Set Theory Discrete Math


Set builder notation translation and cardinality

Given the following:S = {(A, B) | A ⊆ {1, 2, . . . , n}, B ⊆ {1, 2, . . . , n}, |A ∩ B| ≥ 1}, how can I translate this in terms of english and how would one go about finding the cardinality of the... more
Set Theory Sets


If A and B are subsets of the universal set U , then show that

A⊂B⇔A∪B=B , without the use of Venn-Euler diagram.
Set Theory


on set theory

Every resident of a city can speak Hindi or English. If 75 % of the population speaks Hindi and 60% speaks English, then what percentage can speak both the languages ?
Set Theory Math Logic Proofs


Set Theory/Math Logic

Is there any way to prove that   - Every point in A intersect B is greater than or equal to 1?   - The intersection of two sets has a point in commonwith another set?   If there is no way to... more


Define two functions c(x) = max{x - a,0}, p(x) = max{a-x,0}. Prove that c(x) - p(x) = x - a

Define two functions c(x) = max{x - a,0}, p(x) = max{a-x,0}. Prove that c(x) - p(x) = x - a


Let X: [0,1] being in all real numbers be given by X(x) = max{x-0.5,0}. Find the inverse images of all intervals [a,b]

Let X: [0,1] being in all real numbers be given by X(x) = max{x-0.5,0}. Find the inverse images of all intervals [a,b] Due to lack of examples related to the theory, I am unable to properly write... more
Set Theory


J={x|x 4 - 2x is less than equal to 10 ^ x € z}

Convert it into roster form. 
Set Theory Math Proofs


I need help with writing a proof about cardinality. Please look at description for more detail.

Let N^N(Nautral Numbers)={f:f|N->N}.   a. Give two elements of N^N   b. Prove that Aleph Zero <|N^N|
Set Theory


Venn diagram word problem

A survey of 100 school children was taken to determine how they liked their ice cream. It was found that: 55 like vanilla,90 liked at least one of the flavors 50 do not like chocolate,35 liked... more

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