SOLUTION: Can someone please help me with this? I am a little lost and cannot figure this out. Any help is greatly appreciated. Let A = {1, 2, 3, . . . , 10}, and B = {1, 2, 3, . . . , 7}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Can someone please help me with this? I am a little lost and cannot figure this out. Any help is greatly appreciated. Let A = {1, 2, 3, . . . , 10}, and B = {1, 2, 3, . . . , 7}      Log On


   

Question 698378: Can someone please help me with this? I am a little lost and cannot figure this out. Any help is greatly appreciated.
Let A = {1, 2, 3, . . . , 10}, and B = {1, 2, 3, . . . , 7}. How many functions f : A→B satisfy |f (A)| = 4? How many have |f (A)| ≤ 4?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
The set A has 10 elements. The set B has only 7.
In order for an equation to be a function, each value in the domain can map to one and only one value in the range (the vertical line rule).
Yon cannot map 10 domain values onto 7 range values without having at least one point in the domain mapped to more than one in the range.
So for me, the answer is none to both questions. Do you have a different answer? Perhaps the 'back of the book' says something else and we can work backwards from there? it is quite possible I am misunderstanding the original question :)