If $E_1, E_2$ are connected and $A_1\subseteq E_1$ and $A_2\subseteq E_2$ then $(E_1\times E_2)-(A_1\times A_2)$ is connected
39455
Prove that $(X\times Y)\setminus (A\times B)$ is connected
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
39708
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
136654
$(x_1-a_1, x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$
1453
Prove that the graph is connected
146664
The union of two linearly independent subsets
5118
Show that $n ≤ 100$ if $ \{A_1,A_2,... ,A_n\}$ is a set of distinct $3$-element subsets of $\{1, 2,... , 36\}$ such that...
149553
Is it always true that $(A_1 \cup A_2) \times (B_1 \cup B_2)=(A_1\times B_1) \cup (A_2 \times B_2)$
80916
How to prove that if $A\subseteq A\times A$, then $A=\varnothing$?
89659
$H_1 ,H_2 \unlhd \, G$ with $H_1 \cap H_2 = \{1_G\} $. Prove every two elements in $H_1, H_2$ commute
104411
sum of two connected subset of $\mathbb{R}$
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
82578
Show that if $G$ is $2-$connected, then for any two vertices $u$ and $v$ there exists a cycle $C$ such that $u, v \in V (C)$
116538
Proof of Connected Diagrams
12104
How to prove this result involving the quotient maps and connectedness?
118239
If $A, B, C$ are sets prove that $(A\setminus B)\setminus C\subseteq A\setminus(B\setminus C)$
133915
In which case $M_1 \times N \cong M_2 \times N \Rightarrow M_1 \cong M_2$ is true?