Prove that $\{(x,y)\in \mathbb{Z}\times\mathbb{Z}: x^2\equiv y^2 \!\!\!\mod \!\!4\}$ is an equivalence relation
131155
$x\sim y\iff x^2\equiv y^2\pmod{\!6}$ is an equivalence relation.
64656
how do you prove that $A\times (B\setminus C) = (A\times B) \setminus (A\times C)$?
80209
If $X,Y$ are equivalence relations, so is $X \times Y$
73689
A question about the equivalence relation on the localization of a ring.
128989
Is ${\bf Z} \times {\bf Z}$ elementarily equivalent to ${\bf Z}$?
89533
$\mathcal{K}(L^2(\mathbb{R}^m \times \mathbb{R}^n)) = \mathcal{K}(L^2(\mathbb{R}^m)) \otimes \mathcal{K}(L^2(\mathbb{R}^n))$?
119793
Proving that $D_{12}\cong S_3 \times C_2$
39231
Construct a bijection between $\mathbb{Z}^+\times \mathbb{Z}^+$ and $\mathbb{Z}^+$
125008
Define a bijection between $Z^{X \cup Y}$ and $Z^X \times Z^Y$, where $X, Y \in \mathcal{P}(\Omega) $ and $X \cap Y = \emptyset$
109318
Equivalence relation $(a,b) R (c,d) \Leftrightarrow a + d = b + c$
122312
How can I compute $\mathrm{Aut}(\mathbb{Z}/4\mathbb{Z}\times\mathbb{Z}/6\mathbb{Z})$?
88036
Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$
38200
Show that $(\mathbf{a}·\mathbf{a})(\mathbf{b}·\mathbf{b})-(\mathbf{a}·\mathbf{b})^2=(\mathbf{a}\times\mathbf{b})·(\mathbf{a}\times\mathbf{b})$?
77969
Question about proof for $S_4 \cong V_4 \rtimes S_3$
62455
Prove Equivalence Relation in G
11342
Show that conguence $\bmod m\,$ is an equivalence relation
8554
Proof: $\mathrm{adj}(\mathrm{adj}(A)) = (\mathrm{det}(A))^{n-2} \cdot A$ for $A \in \mathbb{R}^{n\times n}$