Proof: A⊆B and B⊆C ⟹ A⊆C
41080
If A, B, and C are set and $A \subset B ,B \subset C \rightarrow A \subset C$
109682
Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
9268
Proving that the Union of Two Compact Sets is Compact
80827
Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
80255
How to prove that $|a-b|<\epsilon$ implies $|b|-\epsilon<|a|<|b|+\epsilon$?
83518
Proving Two sets have same cardinality
25710
$A ⊂ B$ if and only if $A − B = ∅$
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$
146664
The union of two linearly independent subsets
87327
Unions and intersections: $(A \cup B = A ∪ C) \land (A \cap B = A ∩ C) \implies B = C.$
86505
Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
147237
If $A$ and $B$ are compact subsets of $\mathbb R$, then so is $\frac{A}B$.
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.
152817
Proving $\sup B=\inf A$
140668
Union of $2$ set $A, B$ where $ A$ is a subset of $B$
37951
proof detail concerning bijection between a set and its power set