Need help proving A $\subseteq$ B or B $\subseteq$ A.
116527
Validating a proof for necessary and sufficient conditions on sets A & B such that $P(A) \cup P(B) = P(A\cup B)$
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
109682
Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
88064
Prove: $a_n \leq b_n \implies \limsup a_n \leq \limsup b_n$
106564
Suppose $A,B,C$ are sets. Prove that $A\mathbin\triangle B\subseteq C \iff A\cup C=B\cup C$.
132971
Prove that $|a| < b \iff -b<a<b$
83714
$A \in B$ vs. $A \subset B$ for proofs
113083
How to prove a set equality?
6291
Proving something is a linearly independent subset
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
13415
How to show if $A \subseteq B$, then $A \cap B = A$?
46286
Prove if $a\mid b$ and $b\mid a$, then $|a|=|b|$ , $a, b$ are integers.
62077
Prove that if $W_1\subseteq V$ finite-dimensional, then there is $W_2\subseteq V$ such that $V=W_1\oplus W_2$
118239
If $A, B, C$ are sets prove that $(A\setminus B)\setminus C\subseteq A\setminus(B\setminus C)$
48523
Let $A$ be any uncountable set, and let $B$ be a countable subset of $A$. Prove that the cardinality of $A = A - B $