Prove $\dim(A) + \dim(B) = \dim(A+B)$ iff $A \cap B = \{0\}$
53633
Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$
13421
Let $X,Y,Z$ be subspaces of $V$ so that $X$ is a subspace of $Y$. Prove that $Y\cap (X+Z)=X+(Y\cap Z)$
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
19457
Show that: $\inf(A+B) = \inf(A)+ \inf(B)$
106408
Prove that if W is a subspace of a finite dimensional vector space V, then dim(W) ≤ dim(V).
80255
How to prove that $|a-b|<\epsilon$ implies $|b|-\epsilon<|a|<|b|+\epsilon$?
75966
Prove that if $A$ is a set with $m$ elements, $B$ is a set with $n$ elements, and $A \cap B = \emptyset$, then $A \cup B$ has $m+n$ elements.
140446
Prove that $A \smallsetminus (A \smallsetminus B) = A \cap B$
22149
How to prove $dim(Ker (A- \lambda I))=dim (Ker(A^t- \lambda I))$?
67483
Show that $|a-b|<\epsilon \Rightarrow |a|<|b|+\epsilon$
55488
Proving that $\operatorname{codim}(X,Y)=\dim(\mathcal{O}_{X,\eta})$
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
150720
Given that $W$ is a subspace of $V$, prove: $\dim W=\dim V \implies W=V$
103441
Proving $(A\cup B)\cap(B\cup C)\cap(C\cup A)=(A\cap B)\cup (A\cap C)\cup (B\cap C)$?
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
127296
prove that a|b and b|a iff a=+-b