5. 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).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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5. Let A = {a,b} and B = {1,2,3}.
(a) Write out all functions f: A → Busing 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).
6. 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.
Transcribed Image Text:5. Let A = {a,b} and B = {1,2,3}. (a) Write out all functions f: A → Busing 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). 6. 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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