Let A = P({1,2,3,4}). Let f, g and h be the following functions. f : A → A defined by f(X) = X ∩{3,4}.
g : A →Z defined by the greatest element of1 X ifif XX =6= {}{} h : {1,2,3,4}→ A defined by h(x) = {1,2,3,4}−{x}.
1. (i) What is f({2,3,4})?
(ii) What is g({1,2,3})?
(iii) What is h(4)?
(iv) What is f◦h(3)?
2. (i) Is f one-to-one?
(ii) Is g one-to-one?
(iii) Is h one-to-one?
3. (i) What is the range of f?
(ii) What is the range of g?
(iii) What is the range of h?
4. (i) Does f ◦ g exist? If f ◦ g does exist, what is its domain, codomain, and range? (ii) Does g ◦ f exist? If g ◦ f does exist, what is its domain, codomain, and range?
Note: Answers only are required for Question 1, but you should fully justify your answers for the other questions.
