One-to-one and Onto
M117, October 26, 2011 (due October 28, 2011)
Your name:
(1) Draw an example for each of the following (but not necessarily in order):
(a) A function that is one-to-one but not onto.
(b) A function that is onto but not one-to-one.
(c) A function that is both one-to-one and onto.
(d) A function that is neither one-to-one nor onto.
(2) Trade papers with a classmate and determine which of his/her functions satisfy each
of the above criteria.
(3) If f : X → Y is a function, what must be true about the number of elements in X
as compared to the number of elements in Y if:
(a) f is one-to-one but not onto
(b) f is onto but not one-to-one
(c) f is both one-to-one and onto
(d) f is neither one-to-one nor onto