Is U + U' a subspace if U and U' are contained in W?

[nsj]

If U, U ′ are subspaces of V , then the union U ∪ U ′ is almost never a subspace (unless one happens to be contained in the other). Prove that, if W is a subspace, and U ∪ U ′ ⊂ W , then U + U ′ ⊂ W .

This seems fairly simple, but I am stuck on how to go about proving it.

 

[Deveno]

use the closure properties of a subspace.

 

[vlad505]

or you could ask your TA during office hours, Wildcat

 

[Deveno]

if W is a subspace, then for any w1,w2 in W, w1+w2 is also in W.

now, if u is U, and u' is in U', can we say these are in W? why?

 

[spg89]

gimme ur mail id,i will send da pics frm my book...this prove is in my syllabus...

 

[wisvuze]

you know that adding two things from U is okay, you know that adding two things from U' is okay; what happens when you add something from U and something from U'? We already know that W is supposed to be a subspace. What is the definition of the subspace U + U'?