# Thread: theoretical groups proof 1,1

1. ## theoretical groups proof 1,1

V is a vectoric space.
$\displaystyle W_1,W_2\subseteq V\\$
$\displaystyle W_1\nsubseteq W_2\\$
$\displaystyle W_2\nsubseteq W_1\\$
prove that $\displaystyle W_1 \cup W_2$ is not a vectoric subspace of V.

i dont ave the shread of idea on how to tackle it
i only know to prove that some stuff is subspace
but constant mutiplication
and by sum of two coppies

this question here differs a lot

2. Originally Posted by transgalactic
V is a vectoric space.
$\displaystyle W_1,W_2\subseteq V\\$
$\displaystyle W_1\nsubseteq W_2\\$
$\displaystyle W_2\nsubseteq W_1\\$
prove that $\displaystyle W_1 \cup W_2$ is not a vectoric subspace of V.

i dont ave the shread of idea on how to tackle it
i only know to prove that some stuff is subspace
but constant mutiplication
and by sum of two coppies

this question here differs a lot

When you say you "have no idea how to tackle this" you run the risk someone will think you're trying to get somebody to do your hw for you, and that's something many of us won't accept to do.

Try to understand well-well the definitions and the given data in your problem, and then try to understand the following rather good hint:

As $\displaystyle W_1\nsubseteq W_2\,,\,\,\exists w_1\in W_1\setminus W_2$ , and as $\displaystyle W_2\nsubseteq W_1\,,\,\,\exists w_2\in W_2\setminus W_1$

Get a contradiction now by showing that it is impossible that $\displaystyle w_1+w_2\in W_1\cup W_2$

Tonio

3. $\displaystyle W_1$ \ $\displaystyle W_2$ means complement by set theory

wee need to add all the members which exist in W_2 who are not presented in W1
so basically its
$\displaystyle W_1 \cup W_2$
because there intersection is zero

so i cant see a contradiction its very possible that w1+w2 is a part of
$\displaystyle W_1 \cup W_2$

and i cant understand the meaning of w1+w2
there is no such symbol in set theory

?

4. Originally Posted by transgalactic
$\displaystyle W_1$ \ $\displaystyle W_2$ means complement by set theory

wee need to add all the members which exist in W_2 who are not presented in W1
so basically its
$\displaystyle W_1 \cup W_2$
because there intersection is zero

so i cant see a contradiction its very possible that w1+w2 is a part of
$\displaystyle W_1 \cup W_2$

and i cant understand the meaning of w1+w2
there is no such symbol in set theory

?

But we're talking about vector spaces and there's sum of vectors!

Tonio

5. aahh ok i agrree with you
now i see its a sum of vectors

so we have two groups of vectors they dont have common vectors

if we sum both groups we get a new group of vectors
which is lenear combination of both

but what is the relations of this new group with

$\displaystyle W_1 \cup W_2$

$\displaystyle W_1 \cup W_2$ represents all the members from both groups

6. i cant understand what w1+w2 group means

we have two groups of vectors and we sum them

how we some them?
what is the meaning of w1+w2 in the ven diagram?

7. Originally Posted by transgalactic
i cant understand what w1+w2 group means

we have two groups of vectors and we sum them

how we some them?
what is the meaning of w1+w2 in the ven diagram?

Please do read again your definitions and THEN re-read and re-attack this problem. It is already solved but you can't tell since you don't understand the basics, which is something you must do by yourself.

Tonio