Question

in the game of Hearts, four players are each dealt 13 cards from a deck of 52. is this a function? If so, what sets make up the domain and codomain, and is the function injective, surjective bijective, or neither?

Answer 1

Answer:

Let's number the players 1, 2, 3, 4. So if there is a function I would think that 1, 2, 3 and 4 would be the domain. The output would be the 13 cards a player gets, ie f(1) would be the set of 13 cards that player 1 gets. Initially I was going to say that this would not be a function since for one input you get 13 outputs. But here is how you get around that. There are 52C13 different ways of getting dealt 13 cards. If we numbered each possible hand then it seems to be a function. See what you can do with this or tell me why you think it will not work.