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

b) How many equivalent relations are there on A?

My answer: Im not sure about this one. Any help?

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

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

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

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
Before I answer please answer this.
Does you textbook/instructor really use the notation $A\cdot A$ for the cross product of $A$ with itself?
The almost standard notation is $A\times A$.

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 $A\times A$ 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 $A\times A$ 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.