Answer: 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} .
