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lom
Oct26-09, 09:51 AM
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
Mark44
Oct26-09, 10:24 AM
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 \cdown 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
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.
lom
Oct26-09, 10:53 AM
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
Tedjn
Oct26-09, 11:03 AM
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?
lom
Oct26-09, 11:16 AM
W1 and W2 are foreign to each other
there is no intersection between them
Tedjn
Oct26-09, 11:25 AM
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?
lom
Oct26-09, 11:53 AM
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
Tedjn
Oct26-09, 12:31 PM
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?
Mark44
Oct26-09, 01:28 PM
W1 and W2 are foreign to each other
there is no intersection between them

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.