Chapter 2: Q2E (page 183)
Find A + B, where
a)
b)
a) Required matrix is
b) Required matrix is
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let where the domain is the set of real numbers. What is
a) Define what it means for a function from the set of positive integers
to the set of positive integers to be one-to-one
b) Define what it means for a function from the set of positive integers to the set
of positive integers to be onto.
c) Give an example of a function from the set of positive integers to the set of
positive integers that is both one-to-one and onto.
d) Give an example of a function from the set of positive integers to the set of
positive integers that is one-to-one but not onto.
e) Give an example of a function from the set of positive integers to the set of
positive integers that is not one-to-one but is onto.
f) Give an example of a function from the set of positive integers to the set of
positive integers that is neither one-to-one nor onto.
Question: If f and are one-to-one, does it follow that g is one-to-one? Justify your answer.
Compute each of these double sums
a) Show that a partial function from A to B can be viewed as a function from A to B {u} , where u is not an element of B and
b) Using the construction in (a), find the function f* corresponding to each partial function in exercise 77.
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