# Theoretical groups proof 1,1

1. Oct 26, 2009

### lom

V is a vectoric space.

$$W_1,W_2\subseteq V\\$$
$$W_1\nsubseteq W_2\\$$
$$W_2\nsubseteq W_1\\$$
prove that $$W_1 \cup W_2$$ 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 alot

Last edited: Oct 26, 2009
2. Oct 26, 2009

### Staff: Mentor

Differs a lot from what? Is there any other information given in your problem? For example, you have that
$$W_1\nsubseteq W_2$$
and
$$W_2\nsubseteq W_1$$

but are you given anything about
$$W_1 \bigcap W_2$$
?

BTW, the term is "vector space" not vectoric space. No such word as vectoric.

3. Oct 26, 2009

### lom

it differs by its pure theoretic way

i am used to prove that f(x)=0 is a subspace
by the constant multiplication and sum of two copies law
i only know that
$$W_1,W_2\subseteq V\\$$

i have written all the given stuff

4. Oct 26, 2009

### Tedjn

Since you are only given conditions on two subspaces, the only thing you can do next is look at the individual elements. The two conditions $W_1 \not\subseteq W_2$ and $W_2 \not\subseteq W_1$ imply the existence of what elements in these sets?

5. Oct 26, 2009

### lom

W1 and W2 are foreign to each other
there is no intersection between them

6. Oct 26, 2009

### Tedjn

Are you sure that there is no intersection between them? Let's take a step back. What is the actual condition that $W_1 \not\subseteq W_2$?

7. Oct 26, 2009

### lom

its not only
$W_1 \not\subseteq W_2$
its both
$W_1 \not\subseteq W_2$
and $W_2 \not\subseteq W_1$

as for what you say:
$W_1 \not\subseteq W_2$
means that all the members of W1 are not a part W2 group

8. Oct 26, 2009

### Tedjn

No, it does not mean that all the members of W1 are not in W2. It means that there exists a member of W1 that is not in W2. Does that make sense? If so, where can you go from there?

9. Oct 26, 2009

### Staff: Mentor

You can't conclude that from these two statements:
$$W_1\nsubseteq W_2\\$$
$$W_2\nsubseteq W_1\\$$

It's very possible that W1 contains some elements that are in W2, but other elements that aren't in W2. Same thing for the other statement. That's why I asked if you were given that these two sets are disjoint. You said you weren't given that information, and now here you're saying that they are.