Question

seven players are playing 5-card stud. each player initially receives 5 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

Dealing cards in 5-card stud is a function (players & deck in, hands out). It's surjective (all hands reachable) but not injective (different shuffles can give same hand combinations), thus not bijective.

Option B is correct.

Dealing Cards in 5-Card Stud: A Function Analysis

Yes, dealing cards in a 7-player 5-card stud game can be considered a function! Here's a breakdown:

Function: deal_cards(players, deck)

Input (Domain):

players: An integer representing the number of players (7 in this case).

deck: A list representing the remaining cards in the deck (52 initially).

Output (Codomain):

A list of lists, where each sublist represents the 5 cards dealt to a player.

Function Properties:

Injective (One-to-One): No. Different shuffles can lead to the same hand distribution for the players.

Surjective (Onto): Yes. Any possible hand combination for the 7 players can be reached through different shuffles and deals.

Bijective (One-to-One and Onto): No. Since injectivity doesn't hold, the function is not bijective.

Therefore, the function of dealing cards in 5-card stud is surjective, but not injective or bijective.