Proving A and B Finite Sets: Injectivity and Surjectivity of f:A->B

[algonewbee]

Let A and B be finite sets, and let f:A->B be a function. Show that

a)if f is injective, then |A|<=|B|
b)if f is surjective, then |A|>=|B|

 

[HallsofIvy]

Are you in the wrong course? Whoever assigned these problems obviously expects that you know what "injective" and "surjective" mean! What are the definitions of those? How have you tried to apply those definitions? Do you know what it means to say that |A|= |B| for A and B sets? In particular what is the definition of |A|?