Mathematics

Problem

Consider the sets

A=\{0,1,2,3\}

and

B=\{0,1,2,3,4,5,6,7\}

. A relation

R

is defined on

A\times B

by the condition

2x+y=6.

Answer the following questions. a. (i) Write

R

as an explicit set of ordered pairs. b. (ii) Determine the domain and the range of

R

. c. (iii) Verify that

\operatorname{Dom}(R)\subseteq A

and

\operatorname{Ran}(R)\subseteq B

, and state whether either of them equals its parent set.