Give a formal set theoretic argument to prove that, for all sets X, Y and Z, X \ (Y \ Z) = (X \ Y ) ∪ (X ∩ Z) .
52135
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
142631
Show that A has the same cardinality as $A\setminus\{x,y,z\}$
9158
Proving that a propositional theory of any cardinality has an independent set of axioms
105886
A question on the proof of 14 distinct sets can be formed by complementation and closure
109682
Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
17510
Proving a set is an abelian group.
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
151852
How to prove $A \subset B \iff A \cup B = B$
2667
Given $S \hookrightarrow T$ construct $U ≈ T$ disjoint from $S$ in Z set theory?
99927
The closure of $\{ z:|f(z)|<c\}$ is the set $\{z:|f(z)|\leq c\}$.
101803
A\(B∩C) = (A\B) ∪ (A\C) how to prove?
146231
Let X be a set with an associative binary operation ◦ with identity e. Suppose every element of X satisﬁes x ◦ x = e. Prove that ◦ is commutative.
48797
Proving Two Sets are Equal - Infinite Sets - Example
133480
new addition and new multiplication x ⊕ y = x + y − 1, x ⊗ y = x + y − xy on set Z, prove the set Z equipped with these 2 new operation
126633
Is a contradiction enough to prove a set equality to $\varnothing$?
106564
Suppose $A,B,C$ are sets. Prove that $A\mathbin\triangle B\subseteq C \iff A\cup C=B\cup C$.
89506
Union of disjoint sets : Equivalence relations