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 are the domain and codomain? is the function injective, surjective, both (bijective), or neither?

Answer 1

Based on the fact the game of hearts, four players are each dealt 13 cards from a deck of 52

• The domain is the deck of 52 cards
• codomain is 4 players
• function, f(k) maps a card to each player
• It is surjective

This is further explained below.

What is a surjective Function?

A surjective function is a kind of function that exists in mathematics that ensures that any element y may be transferred to element x in such a way that f(x) equals y.

To put it another way, each element that makes up the function's codomain is the mirror image of at least one element that makes up the domain.

Generally, function, f(k) maps a card to each player

And since each player is dealt 13 cards st 13 of the cards are mapped to each player.

It is a function as one card is mapped to one and only one player.

The function is not injective because 13 cards 1 are mapped to one player so it is a many-one function but the injective function does not map two elements to a common clement.

In conclusion, It is surjective as each player is dealt 13 cards. the function is not injective hence rot bijective.

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