A community for students.
Here's the question you clicked on:
 0 viewing
mathmath333
 one year ago
Set Theory
mathmath333
 one year ago
Set Theory

This Question is Closed

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \color{black}{\begin{align} \normalsize \text{A ∩ B = A ∩ C need not imply B = C.} \quad \normalsize \text{ Explain through an example.}\hspace{.33em}\\~\\ \end{align}}\)

Kainui
 one year ago
Best ResponseYou've already chosen the best response.3A = {1} B = {1, 2} C = {1, 3}

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2huh kai was so fast :P

Kainui
 one year ago
Best ResponseYou've already chosen the best response.3Hahaha there could have been a simpler example: A = {} B = {1} C = {2}

Kainui
 one year ago
Best ResponseYou've already chosen the best response.3I think that last example I gave sorta shows that it's almost like this is a lot like multiplying by zero. a*b=a*c This doesn't mean b=c, since a=0 is possible.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0Let A and B be sets. If A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X for some set X, show that A = B.

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2in general any case with \[ A\cap B \neq \varnothing \] does not imply A=C

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2or \(C\cap B \neq \varnothing \)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0i need an example like the previous one

Kainui
 one year ago
Best ResponseYou've already chosen the best response.3ikram needs more owl bucks sry

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2A={1,2,3} B={1,2,3} C={1,2,3,4}

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2:O @Kainui i dont lol

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0is that the example for this que Let A and B be sets. If A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X for some set X, show that A = B.

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2you wanna prove this ?

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2ok example A={1,2,3} B={1.4} C={1,2.3}

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0but C is not there in the question

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2sorry i ment to say x :P

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2now to prove they are two side of the prove 1 show A is a subset of B 2 show B is a subset of A

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.2let \(c\in A \cup X\) so \( c\in A ~or~c\in X \) if c in A then \( c\in B\cup X \) and \( c\in B\) (since c is not in x) thus \(A\subset B\) the other way is alike :P sorry im lazy to type

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.0Is it possible to do something like this? \[ A\cup X=B\cup X\land A\cap X=B\cap X=\emptyset\implies A\cup X\setminus X=B\cup X\setminus X\implies A=B \]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.