README.md

Compatible Birds

Conditions

Two birds A and B are "compatible" if there exist two birds x and y such that A(x) === y and B(y) === x.

Problem

Show that, under the conditions of problem 1, any two birds A and B are compatible.

Solution

We start by composing the arbitrary birds A and B:

const composed = compose(A, B);

Under the conditions of problem 1, we know that every bird is fond of at least one bird. Thus, composed is fond of another bird; let's call it y:

composed(y) === y;
// or...
A(B(y)) === y;

Now, let's name the bird B(y) x:

A(x) === y;

That's our answer: we see that A(x) === y, and we know (from the definition of x) that B(y) === x. Thus, A and B are compatible.

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