Prove that $W_1 \cup W_2$ is subspace of $V$ if and only if $W_1 \subseteq W_2$ or $W_2 \subseteq W_1$
11301
Union of two vector subspaces not a subspace?
62065
Prove that $v_1, \dots v_n$ is a basis of V.
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
76160
Dimension of the sum of two vector subspaces
97049
If $v_1,...,v_m$ are linearly independent, then the span $v_1+w,...,v_m+w$ has dimension $\ge m-1$
150738
Proof of $(A - B) - C = A - (B \cup C)$
149553
Is it always true that $(A_1 \cup A_2) \times (B_1 \cup B_2)=(A_1\times B_1) \cup (A_2 \times B_2)$
104578
Suppose that $V$ is a vector space, and $W$ is a subspace of $V$. If $V$ is finite dimensional, then prove $W$ too must be finite dimensional.
53261
Show that Pn is an (n+1)-dimensional subspace
92774
Prove that a linear subspace of $C([0,1])$ is closed
14713
$X=(-\infty,0]\cup\left\{{1\over n}:n\in\mathbb N\right\}$ with subspace topology Then
90525
The subspace of $\ell_2$
16512
Product of $T_1$ spaces is $T_1$
150720
Given that $W$ is a subspace of $V$, prove: $\dim W=\dim V \implies W=V$
18921
Linear Transformations: Proving 1 dimensional subspace goes to 1 dimensional
45337
Suppose that $V, W$ are closed in $X$ and that $V\cap W, V\cup W$ are connected. Show that $V$ and $W$ are connected.
143979
How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?