# Thread: equivalent relations help

1. ## equivalent relations help

Hey guys, having trouble with the following question.
Let A = {1,2,3,4},

a) how many relations are there on A?

My answer: $\displaystyle \mathcal{P}(A \cdot A)$ = $\displaystyle 2^{4 \cdot 4}$ = $\displaystyle 2^{16}$

b) How many equivalent relations are there on A?

2. Originally Posted by jvignacio
Let A = {1,2,3,4},
a) how many relations are there on A?

My answer: $\displaystyle \mathcal{P}(A \cdot A)$ = $\displaystyle 2^{4 \cdot 4}$ = $\displaystyle 2^{16}$ CORRECT

b) How many equivalent relations are there on A?
Does you textbook/instructor really use the notation $\displaystyle A\cdot A$ for the cross product of $\displaystyle A$ with itself?
The almost standard notation is $\displaystyle A\times A$.

For the help. There is a one-to-one correspondence between the partitions of the set and the equivalence relations on the set.
You want to find the fourth Bell number.

3. Originally Posted by Plato
Does you textbook/instructor really use the notation $\displaystyle A\cdot A$ for the cross product of $\displaystyle A$ with itself?
The almost standard notation is $\displaystyle A\times A$.

For the help. There is a one-to-one correspondence between the partitions of the set and the equivalence relations on the set.
You want to find the fourth Bell number.
No they use $\displaystyle A\times A$ but I didnt know the latex symbol for x. Now I do

Not sure what you mean by fourth Bell number.....

4. Originally Posted by jvignacio
No they use $\displaystyle A\times A$ but I didnt know the latex symbol for x. Now I do

Not sure what you mean by fourth Bell number.....
Do a web search for Bell Numbers.