Let $A \subseteq \mathbb{R}$ and $|A|=\omega$, prove $|\mathbb{R}\setminus A| = 2^\omega$.
3902
Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
80916
How to prove that if $A\subseteq A\times A$, then $A=\varnothing$?
142631
Show that A has the same cardinality as $A\setminus\{x,y,z\}$
92639
Prove that the family of open sets in $\mathbb{R}$ has cardinality equal to $2^{\aleph_0}$
108642
$e^A$, where $A= \begin{bmatrix} 0 & \omega \\ -\omega& 0 \end{bmatrix}$
136980
Prove there exists $a\in \Bbb{R}$ such that $f'(a)=0$.
46056
If $\mathcal{E}$ are subsets of $X$ and $A \subset X$. Show that $\mathcal{A}\mathcal{(E \cap}$ A)=$\mathcal{A}\mathcal{(E)} \cap$ A
140446
Prove that $A \smallsetminus (A \smallsetminus B) = A \cap B$
93684
Show that $\mu (E \setminus A)>0$ if $A$ is a nonmeasurable subset of $X$ and $A \subseteq E$, $E$ is measurable.
155579
Show that $End_A(A)$ = {$r_a$ | $a ∈ A$}
157218
If $E\subseteq X$ is connected, $E\cap A\neq\emptyset$ and $E\cap(X\setminus A)\neq\emptyset$ then $E\cap\partial A\neq\emptyset$
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
55461
How to prove that if $a$ belongs to $\mathbb R$, such that $0\leq a \leq\epsilon$, then $a = 0$
118239
If $A, B, C$ are sets prove that $(A\setminus B)\setminus C\subseteq A\setminus(B\setminus C)$
52135
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
151928
How to prove that $N\setminus A$ is finite?
158498
$A\subset \mathbb{R}$ with more than one element and $A/ \{a\}$ is compact for a fixed $a\in A$