MATH SOLVE

3 months ago

Q:
# 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?

Accepted Solution

A:

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 thatthe domain of a function is the set of all the first elements in the ordered pairs, so the domain of the function R will beD = {a, b, c, d, e}.(c) We know thatthe range of a function is the set of all the second elements in the ordered pairs, so the domain of the function R will beR = {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} .