Binary Relations Between Sets A and B: Quick Question

[ktheo]

Homework Statement

True or False: Given that A = {a,b,c} and B={0,1,2,3,4}, there are 32768 binary relations from A to B

I assume there is some simple way to tell how many relations there are given two different sets, but I don't know it. Factorials? Powers? I'm not sure what.

 

[pasmith]

Homework Statement

True or False: Given that A = {a,b,c} and B={0,1,2,3,4}, there are 32768 binary relations from A to B

I assume there is some simple way to tell how many relations there are given two different sets, but I don't know it. Factorials? Powers? I'm not sure what.

A "binary relation from A to B" is formally a subset of $A \times B$, so the number of such relations is the number of subsets of $A \times B$.

 

[Dick]

Homework Statement

True or False: Given that A = {a,b,c} and B={0,1,2,3,4}, there are 32768 binary relations from A to B

I assume there is some simple way to tell how many relations there are given two different sets, but I don't know it. Factorials? Powers? I'm not sure what.

Try and work it out. How many total ordered pairs are there in AxB? Now each ordered pair can either be in the relation or not.