Question 1: Let A= {a, b} and let S be the set of all strings with alphabet A. D

Question

Question 1:

Let A= {a, b} and let S be the set of all strings with alphabet A. Define f: S -> S as follows:

For any string ?, define f(?) = the string resulting by replacing all a's by b's and all b's by a's in the string.

Select all true statements below:

f is an onto function

For all input strings x, f(x) = f(f(x))

f has an inverse

f is a one-to-one function

Question 2:

All of the functions below follow the equation

f is an onto function

For all input strings x, f(x) = f(f(x))

f has an inverse

f is a one-to-one function

Explanation / Answer

Question 4 options

f is an onto function

f has an inverse

f is a one-to-one function

Question 2 options:

1)f: Z -> Z not one-to-one: not onto

2)f: R+ -> R+ one-to-one; onto

3)f: R+ -> R one-to-one: not onto

4)f: R -> R(nonneg) not one-to-one; onto

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