How to prove that $B$ is uncontable if $A$ is uncontable, $A\subseteq B$?
71922
Prove Uncountable set minus a countable set is uncountable
83842
Alternate proofs (other than diagonalization and topological nested sets) for uncountability of the reals?
123149
Prove that $E$ is disconnected iff there exists two open disjoint sets $A$,$B$ in $X$
101803
A\(B∩C) = (A\B) ∪ (A\C) how to prove?
157513
How can I prove that these sets are countable infinite?
19856
Prove that a subset of a separable set is itself separable
81618
Prove $||a|-|b| | \leq |a-b|$
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
107540
how to prove that $abc$ and $cba$ do not necessarily have the same order?
132971
Prove that $|a| < b \iff -b<a<b$
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
140799
Prove that there exist uncountable family of subsets of $\mathbb{N}$ which is linearly (totally) ordered by relation of inclusion.
50939
If $A$ and $B$ are nonempty sets, prove that $A \times B = B \times A$ if and only if $A = B$
39708
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
127656
How to prove that if $A$ is infinite and $B$ is finite, then $|A\cup B|=|A|$?
113344
How do we prove that something is unprovable?
125164
How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?