How to show that $\bigcup_{i\in \emptyset} A_i=\emptyset$ and $\bigcap_{i\in \emptyset}A_i=X$?
36881
Empty intersection and empty union
858
Is $\{\emptyset\}$ a subset of $\{\{\emptyset\}\}$?
149553
Is it always true that $(A_1 \cup A_2) \times (B_1 \cup B_2)=(A_1\times B_1) \cup (A_2 \times B_2)$
109219
How do the sets $\emptyset\times B,\ A\ \times \emptyset, \ \emptyset \times \emptyset $ look like?
157218
If $E\subseteq X$ is connected, $E\cap A\neq\emptyset$ and $E\cap(X\setminus A)\neq\emptyset$ then $E\cap\partial A\neq\emptyset$
150825
Is an empty set equal to another empty set?
140446
Prove that $A \smallsetminus (A \smallsetminus B) = A \cap B$
78763
Prove that $ S=\{0\}\cup\left(\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}\right)$ is a compact set in $\mathbb{R}$.
61066
Prove: $(A\rightarrow B),(A\rightarrow C)\rightarrow B, \mapsto_{HPC} B $
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
123613
Double Complement of a set proof
5132
Given $A\cap \overline{B}\neq \emptyset$, prove $A\cup B$ connected.
144502
Showing that $A\cap B = A\setminus (A\setminus B)$
155233
$A=\emptyset $ if and only if $B = A \bigtriangleup B$
27899
Can we prove the existence of $A\cup B$ without the union axiom?
64586
How to prove that $\neg((A\cap B)\cup (\neg A \cap C)) = (A\cap\neg B)\cup (\neg A\cap \neg C)$