Let $A$ and $B$ be sets. Suppose that there is some set $X$ such that $A \cap X = B \cap X$ and $A \cup X = B \cup X$. Show that $A = B$.
7416
Let $ A $, $ B $ and $ C $ be sets. If $ A \cup B = A \cup C $ and $ A \cap B = A \cap C $, then show that $ B = C $.
101803
A\(B∩C) = (A\B) ∪ (A\C) how to prove?
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.
13132
If the union of two sets is contained in the intersection, then one is contained in the other ($[A\cup B\subseteq A\cap B]\implies A \subseteq B$)
10909
$|A \cup B| = \mathfrak{c}$, then $A$ or $B$ has cardinality $\mathfrak{c}$.
12472
Let $X$ and $Y$ be countable sets. Then $X\cup Y$ is countable
119084
How many ordered pairs $(A,B)$ they are if $A$ and $B$ are subsets of $\{ 1,2,3,4,5 \}$ such that $A \cap B = \{1\}$?
70307
$(A\cap B)\cup C = A \cap (B\cup C)$ if and only if $C \subset A$
80759
Proving $A\times (B\cap C)=(A \times B)\cap (A\times C)$.
13415
How to show if $A \subseteq B$, then $A \cap B = A$?
95935
Prove A = $(A \cap B) \cup (A \cap B^c)$ using the distributive and associative law.
43068
Let A and B be sets. Show that A is a subset of B if and only if for any set C, one has A union C is a subset of B union C.
142993
Proof of A ⊆ C and B ⊆ C ⇔ A ∪ B ⊆ C
43310
Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
76826
Are there sets $A$ and $B$ such that $A \in B$ and $B \in A$?
130156
Image of the union and intersection of sets.
90434
Prove for every two sets $A$ and $B$ that $A-B$, ${B-A}$ and $A \cap B$ are pairwise disjoint.