44 Answered Questions for the topic Set Theory

#### 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...
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03/20/22

#### 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) \...
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#### 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?

03/13/22

#### 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.

02/25/22

#### 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...
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10/05/21

#### 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...
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10/21/20

#### 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.

05/01/19

#### 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...
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03/18/19

#### 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...
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Set Theory

03/12/19

#### If a and b are mutually exclusive events with p(A) =0.3 ,p(B)= 0.5 ,then p(AUB) is equal to what ?

Set Theory Statistics

03/02/19

#### What is the Infimum and Supremum (if there are any) of the following set: {x^4 : x is an element of the real numbers}

Set Theory

11/28/18

#### 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...
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Set Theory Algebra Word Problem

09/10/18

#### 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...
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Set Theory Discrete Math

06/30/18

#### 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...
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Set Theory Sets

06/25/18

#### 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

04/28/18

#### 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

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...
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01/08/18

#### 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

01/08/18

#### 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...
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Set Theory Math Proofs

11/20/17

#### 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

06/28/17

#### 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...
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