Prove that $U⊆W_1$ or $ U⊆W_2$ if $U⊆W_1∪W_2$.
11301
Union of two vector subspaces not a subspace?
133087
Prove that, if $\{u,v,w\}$ is a basis for a vector space $V$, then so is $\{u+v, v+w, u+v+w\}$.
151852
How to prove $A \subset B \iff A \cup B = B$
18223
Prove that the union of two disjoint countable sets is countable
133915
In which case $M_1 \times N \cong M_2 \times N \Rightarrow M_1 \cong M_2$ is true?
12857
Induction proof: $S$ contains powers of 2 and predecessors implies $S={\bf N}$
127397
$z\overline{w}\ne 1 $ Prove that $|\frac{w-z}{1-\overline{w}z}|\le 1|$ if $|z|\le 1$ and $|w|\le 1 $
9149
Any $B \subset \{10,11,...,99\}$, with $|B| =10$ has two subsets such that $\sum_{a \in B_1} a = \sum_{b \in B_2} b$
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
112631
Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
102168
Prove that there exists disjoint open subsets $U,V$ of $X$ such that $x \in U$ and $B \subseteq V$.
75387
A proof that $1=2$. May I know why it’s false?
112084
Proof of a formula for the power set of a union of two sets
134914
Let $A,B$ and $U$ be sets so that $A\subseteq U$ and $B\subseteq U$. Prove that $A\subseteq B$ iff $(U\setminus B)\subseteq(U\setminus A)$.
140440
Proving $(A\times C)\cup(B\times D)\subseteq(A\cup B)\times(C\cup D)$
101803
A\(B∩C) = (A\B) ∪ (A\C) how to prove?
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$