Question

Prove:
Let A, B.C and D be sets
If C is a subset of A and D a subset of B then the intersection of C and D is a subset of the intersection of A and B
(sorry I suck at latex)

Answer 1

@nbouscal can u take a look?

Answer 2

Like ill show u what i have and maybe u can help me out
Suppose \[x \epsilon C \cap D\] then by definition of a subset \[x \epsilon A\] and \[ x \epsilon B\] By definition of intersection \[ x \epsilon A \cap B\] Therefore \[C \cap D \subset A \cap B\]

Answer 3

@malevolence19 can u plz check this out?

Answer 4

like maybe i shldnt have assumed that \[ x \epsilon C \cap D\]

Answer 5

@KingGeorge can u help me?

Answer 6

This is just to help me think.

Given \(C\subseteq A\), \(D\subseteq A\), prove that \(C\cap D \subseteq A\cap B\).

Answer 7

So suppose \(x\in C\cap D\). Then \(x\in C\) and \(x\in D\). Since \(C\subseteq A\), and \(D\subseteq B\), we know that \(x\in A\) and \(x\in B\). Hence, \[x\in A\cap B\implies C\cap D\subseteq A\cap B\]

Answer 8

What you wrote down pretty much looks correct to me.

Answer 9

ohhh yay simple as that

Answer 10

buttt i have a question

Answer 11

when using latex how did u get it to be on one line everytime i used it it started a new line

Answer 12

Use \(\color{red}{\text{\ ( \)}}\) without that space between \ and (

Answer 13

Thanks :DDDDDDD U R AWESOME

Answer 14

You're welcome =D