Question

Exercise 9.

In the questions below you can describe the relations/functions either by drawing a diagram, by a formula, or by listing the ordered pairs. Explain your solutions.
(i) Give an example of two sets A and B and a relation R from A to B which is not a function.
(ii) [hard] Find a set A, |A| = 4 and define a bijective function between A and P(A)? If such a set doesn’t exist give a reason.

Exercise 11. (i) Give an example of a function f : N → N which is total and injective, but not surjective. If such a function doesn’t exist, give a reason. Define the inverse function of the function f. If such a function doesn’t exist, give a reason. (ii) Give an example of a function f : N→N which is partial, injective, and surjective. If such a function doesn’t exist, give a reason.

Answer 1