Chapter 2: Q54E (page 137)
What subsets of a finite universal set do these bit strings represent?
a)The string with all zeros
b) The string with all ones
a) The string with all zeroes, the set is empty set
b) The string with all ones, the set is universal set.
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Suppose that f is a function from A to B, where A and B are finite sets with |A| = |B|. Show that f is one-to-one if and only if it is onto.
Suppose that f is an invertible function from Y to Z and g is an invertible function from X to Y. Show that the inverse of the composition f g is given by
Specify a codomain for each of the functions in Exercise 16. Under what conditions is each of these functions with the codomain you specified onto?
Question:
a. Give an example to show that the inclusion in part (b) in exercise 40 may be proper.
b.Show that if f is one-to-one, the inclusion in part(b) in exercise 40 is an equality.
Determine whether each of these functions is a bijection from R to R.
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