Relations in Math - Definition & Examples

$$\text{How Oscars Could Have Worked}$$

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Every February, people make their predictions and place their bets about which movies will win. Every Oscars, some leave with tears of joy and some leave with tears of disappointment. Could there be a funky, mathematical way to give out awards such that everyone is happy?

Say we have a set of awards and a set of films. Each crew of the films names certain awards they are particularly interested in getting. Since we know one award cannot be given to multiple films, we can only give a limited amount of awards to each film. Let’s look at a concrete example to get a better sense of this idea.

Say there are a total of 4 movies and 10 awards. Each movie names a few desired awards. Is there a way to assign awards, so each movie gets 2 awards they want? Here is a map showing their preferences.