Let sets A and B be defined as follows: A = {Java, Python, R} B = {Tom, Bo} a. L

Question

Let sets A and B be defined as follows: A = {Java, Python, R} B = {Tom, Bo} a. List as a set of ordered pairs one 1-1 function from A to B, or explain why no such function exists. b. List as a set of ordered pairs one onto function from A to B, or explain why no such function exists. c. Let f:B rightarrow A be given by this set of ordered pairs: f = {(Tom, Java), (Bo, Python)} If f has an inverse function, call it g and list g as a set of ordered pairs. If f has no inverse function, explain why not.

Explanation / Answer

4.

a) No such function exists : The function is injective (one-to-one) if every element of the codomain is mapped to by at most one element of the domain.1-to-1 function is possible only if number of elements in set A(domain) is less than or equal to number of elements in Set B(codomain).

b) f = {(Java,Tom),(Python,Bo),(R,Bo)}

c)f-1 =  g = {()Java,Tom,(Python,Bo)}

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