(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This is a problem from chapter 1.3 of Linear Algebra by F/I/S.

Let [itex]W_{1}[/itex] and [itex]W_{2}[/itex] be subspaces of a vector space V. Prove that [itex]W_{1}[/itex] [itex]\cup[/itex] [itex]W_{2}[/itex] is a subspace of V iff [itex]W_{1}[/itex][itex]\subseteq[/itex][itex]W_{2}[/itex] or [itex]W_{2}[/itex] [itex]\subseteq[/itex] [itex]W_{1}[/itex].

2. Relevant equations

See attempt at solution.

3. The attempt at a solution

My proof goes as such:

If [itex]W_{1}[/itex][itex]\subseteq[/itex][itex]W_{2}[/itex] then the union of those subspaces is [itex]W_{2}[/itex], therefore, by the given, it the union is a subspace of V.

The same logic is used to argue the other subset.

I'm not sure if this is correct, and additionally, I'm not sure if its a logical proof. I feel it is a little cyclical maybe. Thanks for all the help, I'm having a tough time with this text.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Proof involving subsets of a vector space

**Physics Forums | Science Articles, Homework Help, Discussion**