$\mid{B}\mid=\aleph_0 , A\cap{B}=\emptyset$. Prove $\mid{A} \cup B \mid\,=\,\mid{A} \mid$
91163
Let the set S be infinite, and the set T countably infinite. Show that S and S U T have the same cardinality
150738
Proof of $(A - B) - C = A - (B \cup C)$
125008
Define a bijection between $Z^{X \cup Y}$ and $Z^X \times Z^Y$, where $X, Y \in \mathcal{P}(\Omega) $ and $X \cap Y = \emptyset$
77164
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
80421
Show that $a - b \mid f(a) - f(b)$
70307
$(A\cap B)\cup C = A \cap (B\cup C)$ if and only if $C \subset A$
144266
set theory proof of $A\cap B = A \setminus(A\setminus B)$
143979
How can I prove that $|A| + |B| = |A\cup B| + |A\cap B|$?
10236
Show that $a^n \mid b^n$ implies $a \mid b$
138069
Proof that $\bigcap_{a\in A} \bigg(\, \bigcup_{b\in B} F_{a,b} \, \bigg) = \bigcup_{f\in ^AB} \bigg(\, \bigcap_{a \in A} F_{a,f(a)}\,\bigg) $
52787
If $\bigcup F = A$ then $A\in F$ then prove that $A$ has exactly one element
137707
How to prove that $(A\cup B) \cap C \subseteq A\cup (B\cap C)$
120010
Show that $\aleph_{\alpha}^{\aleph_{1}} = \aleph_{\alpha}^{\aleph_{0}}\cdot 2^{\aleph_1}$
52135
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
10909
$|A \cup B| = \mathfrak{c}$, then $A$ or $B$ has cardinality $\mathfrak{c}$.
86977
If $\cup \mathcal{F}=A$ then $A \in \mathcal{F}$. Prove that $A$ has exactly one element.
46240
Show that if $A$ and $B$ are sets, then $(A\cap B) \cup (A\cap \overline{B})=A$.