# Thread: number of relations between two sets

1. ## number of relations between two sets

The total number of relations that can be defined from a set A to a set B
is the number of possible subsets of A × B. If n(A ) = p and n(B) = q, then
n (A × B) = pq and the total number of relations is 2pq (we say).

However, doesn't 2pq. also count the null set of ordered pairs as a relation? whether to count a null set of ordered pairs as a relation?

kindly enlighten me.

with regards

Aranga

2. ## Re: number of relations between two sets

Well, what, exactly, is your definition of "relation"? Does the empty set fit that definition?

3. ## Re: number of relations between two sets

I am asking generally. Suppose if set A = {a,b,c} and set B = {1,2,3} What are all the possible relations between A and B.

4. ## Re: number of relations between two sets

Originally Posted by arangu1508
I am asking generally. Suppose if set A = {a,b,c} and set B = {1,2,3} What are all the possible relations between A and B.
Again, It depends on the definition of Binary relation you use.
Look at this definition at Wolfram's MathWorld.
There is says "ANY subset of $A\times B$. Thus that includes $\emptyset$.

5. ## Re: number of relations between two sets

You need to specify the binary relation you use. Because the result may depend on it.

6. ## Re: number of relations between two sets

Originally Posted by SummerStudy
You need to specify the binary relation you use. Because the result may depend on it.
That is a false statement. The question asks "How many relations are there between two sets(finite): $A\to B$
Your [b]definition of "any relation" can make a difference in the number, but not a particular relation.