$(a,b)R(x,y) \iff ay=bx$ is an equivalence on $\Bbb Z \times (\Bbb Z\setminus\{0\})$
73334
Proving this relation is transitive
99911
How to show that if $x=(p,q)$ and $y=(p',q')$ then $x \sim y $ if $pq'=p'q$ is an equivalence relation?
31391
bijection between $\mathbb{N}$ and $\mathbb{N}\times\mathbb{N}$
98630
For all $x,y\in\mathbb{R}$ define that $x\equiv y$ if $x^{2}=y^{2} $; prove $\equiv$ is an equivalence relation.
150064
Cardinality of "$x-y\in\Bbb Q$"-equivalence class of $1/\sqrt2$
142631
Show that A has the same cardinality as $A\setminus\{x,y,z\}$
53915
prove that $a \equiv b \mod m$ is an equivalence relation on the integers
21807
on proving bac-cab rule, $\vec{A} \times ( \vec{B} \times \vec{C})= \vec{B} (\vec{A} \cdot\vec{C})- \vec{C}(\vec{A}\cdot\vec{B})$
62455
Prove Equivalence Relation in G
60140
Proof of Equivalence Relation $R=\{(a,b)\in\Bbb N^2: 5\mid (2a+3b)\}$
85713
Showing Parallelism is an equivalence relation in $\Bbb R ^2$
109710
Bijection between $\mathbb N \times \mathbb N$ and $\mathbb N$
71767
What is the difference between $\Bbb{R^n}\times\Bbb{R^m}$ and $\Bbb{R^{m+n}}$?
64656
how do you prove that $A\times (B\setminus C) = (A\times B) \setminus (A\times C)$?
75604
Proof that $\partial(A\times B) = ((\partial A)\times B)\cup (A\times(\partial B))$
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
130137
How to define a Bijection between $(A^B)^C$ and $A^{B \times C}$