Show that, if $S_1$ and $S_2$ are subsets of a vector space $V$ such that $S_1 \subseteq S_2$, then $span(S_1) \subseteq span(S_2)$.
7462
If X and Y are two sets of vectors in a vector space V, and if X $\subset$ Y, then is span X $\subset$ span Y?
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
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.
148413
Proving $S_n$ is generated by the set $\{(1\text{ }2),(2\text{ }3),\cdots,(n-1\text{ }n)\}$ of $n-1$ transpositions.
46056
If $\mathcal{E}$ are subsets of $X$ and $A \subset X$. Show that $\mathcal{A}\mathcal{(E \cap}$ A)=$\mathcal{A}\mathcal{(E)} \cap$ A
76188
Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
150166
What is $P([a_1,b_1]\times [a_2,b_2]\times...\times[a_k,b_k])$
99300
Prove if $W \subset V$ is a subspace such that $T(W)\subset W$, then $V/W$ is finite-dimensional.
41013
Subspace of $C^3$ that spanned by a set over C and over R
89058
Question on finite Vector Spaces, injective, surjective and if $V$ is not finite
144693
Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
83996
For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$
132487
Proving that if $V$ is an inner product space and $U_1, U_2$ are subsets, then $U_1 \subset U_2$ if and only if $U^{\perp}_2 \subset U^{\perp}_1$
87692
Basis and dimension of vector space
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
13415
How to show if $A \subseteq B$, then $A \cap B = A$?