Mathematics

Problem

Consider the non–empty sets

A=\{1,3,5\}

and

B=\{2,4,6\}

. A subset

R

A\times B

is defined by

R=\{(a,b)\in A\times B\mid a+b \text{ is odd}\}.

Answer the following questions: a. (i) Explain why

R

is a relation from

A

B

. State clearly the condition that every ordered pair in

R

must satisfy. b. (ii) Without listing all ordered pairs of

A\times B

, describe in words the rule that generates the ordered pairs in

R

. Justify your description. c. (iii) Determine the domain and range of

R

, giving reasons for each element you include.