1) for a = {a, b, c, d, e} and b = {yellow, orange, blue, green, white, red, black}. a) define a relation r from a to b that is a function and contains at least 4 ordered pairs. b) what is the domain of this function? c) what is the range of this function?

 The required function is R =  {(a, blue), (b, green), (c, green), (d, white), (e, black)}, domain, D = {a, b, c, d, e} and range, R = {blue, green, white, black} .

Step-by-step explanation: We are given the following two sets :

A = {a, b, c, d, e}

and

B = {yellow, orange, blue, green, white, red, black}.

We are to define a relation R from A to B that is a function and contains at least 4 ordered pairs. Also, to find the domain and range of the function.

(a) Let the function R be defined as follows :

R = {(a, blue), (b, green), (c, green), (d, white), (e, black)}.

Since R contains five ordered pairs, so this will fulfill our criterion. Also, since each first element is associated with one and only one second element, so R defines a function.

(b) We know that

the domain of a function is the set of all the first elements in the ordered pairs, so the domain of the function R will be

D = {a, b, c, d, e}.

(c) We know that

the range of a function is the set of all the second elements in the ordered pairs, so the domain of the function R will be

R = {blue, green, white, black}.

Thus, the required function is R =  {(a, blue), (b, green), (c, green), (d, white), (e, black)}, domain, D = {a, b, c, d, e} and range, R = {blue, green, white, black} .