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2. Let A = {a,b} and B = {1,2,3}. (a) Write out all functions f :...

2. Let A = {a,b} and B = {1,2,3}.

(a) Write out all functions f : A → B using two-line notation. How many different functions are there, and why does this number make sense? (You might want to consider the multiplicative principle here).

(b) How many of the functions are injective? How many are surjective? Identify these (circle/square the functions in your list).

(c) Based on your work above, and what you know about the multiplicative principle, how many functions f : A → B are there if |A| = 5 and |B| = 7? How many of those are injective? How many are surjective? Explain your answers.

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