How many functions are there from A to B

[tysonk]

How many functions are possible from A to B?

A={a,b,c}
B={x,y}

When I did this by counting the possible functions I could only find 7. But the "uncommon" 7 makes me feel like I missed a case. If someone could confirm that would be appreciated.

 

[HallsofIvy]

Well, how did you get "7"?

Since there are no restrictions on the function, such as "one-to-one" or "onto", a can be mapped into either x or y, so can b, and so can c so there are clearly $2^3= 8$ such functions. Are you saying that you tried to list them and only got 7?

I get:
{(a, x), (b, x), (c, x)}
{(a, x), (b, x), (c, y)}
{(a, x), (b, y), (c, x)}
{(a, x), (b, y), (c, y)}
{(a, y), (b, x), (c, x)}
{(a, y), (b, x), (c, y)}
{(a, y), (b, y), (c, x)}
{(a, y), (b, y), (c, y)}

 

[vickypak]

members of B power members of A