Write the Relation in Set Builder Form and Roster Form
Question
Figure 2.15 shows a relationship between the sets \(P\) and \(Q\).
Write the relation in:
(i) set builder form
(ii) roster form
Also find its domain and range.
Solution
From the diagram,
\[ 5\to3,\quad 6\to4,\quad 7\to5 \]
Therefore,
\[ R=\{(5,3),(6,4),(7,5)\} \]
(i) Set Builder Form
\[ \boxed{ R=\{(x,y):y=x-2\} } \]
(ii) Roster Form
\[ \boxed{ R=\{(5,3),(6,4),(7,5)\} } \]
Domain
\[ \boxed{ \{5,6,7\} } \]
Range
\[ \boxed{ \{3,4,5\} } \]