$\text{a}$, $\text{c}$ og $\text{d}$ er relatert til $\text{c}$ gjennom ekvivalensrelasjonen, så $[\text{c}] = \left\{ \text{a}, \text{c}, \text{d} \right\}$.
Eksempel: Ekvivalensklasse
Test deg selv
La $\sim$ være ekvivalensrelasjonen
$$\big\{ \langle \text{a},\text{a} \rangle, \langle \text{b},\text{b} \rangle, \langle \text{c},\text{c} \rangle, \langle \text{d},\text{d} \rangle, \langle \text{a},\text{c} \rangle, \langle \text{c},\text{a} \rangle, \langle \text{c},\text{d} \rangle, \langle \text{d},\text{c} \rangle, \langle \text{a},\text{d} \rangle, \langle \text{d},\text{a} \rangle \big\}$$
på mengden $M = \big\{ \text{a}, \text{b}, \text{c}, \text{d} \big\}$.
Hvilke elementer finnes i $[\text{c}]$ (ekvivalensklassen til $\text{c}$)?
Test deg selv
La $\sim$ være ekvivalensrelasjonen
$$\big\{ \langle \text{a},\text{a} \rangle, \langle \text{b},\text{b} \rangle, \langle \text{c},\text{c} \rangle, \langle \text{d},\text{d} \rangle, \langle \text{a},\text{c} \rangle, \langle \text{c},\text{a} \rangle, \langle \text{c},\text{d} \rangle, \langle \text{d},\text{c} \rangle, \langle \text{a},\text{d} \rangle, \langle \text{d},\text{a} \rangle \big\}$$
på mengden $M = \big\{ \text{a}, \text{b}, \text{c}, \text{d} \big\}$.
Hvor mange elementer er det i $M/\sim$ (kvotientmengden til $M$)?
De to elementene i kvotientmengden er de to ekvivalensklassene. $M/\sim = \left\{ \left\{ \text{a}, \text{c}, \text{d} \right\}, \left\{ \text{b} \right\} \right\}$
Test deg selv
La $\sim$ være ekvivalensrelasjonen
$$\big\{ \langle \text{a},\text{a} \rangle, \langle \text{b},\text{b} \rangle, \langle \text{c},\text{c} \rangle, \langle \text{d},\text{d} \rangle, \langle \text{a},\text{c} \rangle, \langle \text{c},\text{a} \rangle, \langle \text{c},\text{d} \rangle, \langle \text{d},\text{c} \rangle, \langle \text{a},\text{d} \rangle, \langle \text{d},\text{a} \rangle \big\}$$
på mengden $M = \big\{ \text{a}, \text{b}, \text{c}, \text{d} \big\}$.
Hva blir $[\text{a}]$?
$\text{a}$ og $\text{d}$ er relatert til hverandre gjennom ekvivalensrelasjonen, så ekvivalensklassene deres er like. Altså er $[\text{a}] = [\text{d}]$.