How to find equivalence class of this relation?

Question

In solving this problem:

Let $R$ be an equivalence relation on the set $A = \{a,b,c,d\}$, defined by partitions $P = \{\{a,d\},\{b,c\}\}$. Determine the elements of the equivalence relation and also find the equivalence classes of $R$.

I found the elements as asked by the first part of the question. $$ R = \{ \{a,a\}, \{a,d\}, \{d,a\}, \{d,d\}, \{b,b\}, \{c,c\}, \{c,b\}, \{b,c\} \} $$

Not sure about equivalence class.

Do you know the definition of equivalence classes? They are really really really tightly connected to the partitions... — 5xum, Oct 13 '15 at 15:57
hint: start to write down the full equivalence class of $a$. — Max, Oct 13 '15 at 15:57

score 1 · Answer 1 · answered Oct 13 '15 at 16:14

1

https://www.youtube.com/watch?v=rFexPRbJLlw

After seeing this video, the answer is:

[a] = [d] = {a,d}

[b] = [c] = {b,c}

answered Oct 13 '15 at 16:14

Code Man

119

score 1 · Answer 2 · answered Oct 13 '15 at 16:49

1

Give that partition, you ought to define $\sim$ on $A$ as $$x\sim y\quad\mbox{iff ``$x$ and $y$ are in the same subset"}.$$ So it is easy to see that there are only two equivalences classes: those mentioned by Code Man.

answered Oct 13 '15 at 16:49

janmarqz

10,538

How to find equivalence class of this relation?

2 Answers2