Relation on \(A\) Defined by “\(b\) is Exactly Divisible by \(a\)”
Question
Let \[ A=\{1,2,3,4,5,6\} \]
Let \(R\) be a relation on \(A\) defined by
\[ R=\{(a,b):a,b\in A,\ b \text{ is exactly divisible by } a\} \]
(i) Write \(R\) in roster form
(ii) Find the domain of \(R\)
(iii) Find the range of \(R\)
Solution
(i) Roster Form
\[ R= \{ (1,1),(1,2),(1,3),(1,4),(1,5),(1,6), \]
\[ (2,2),(2,4),(2,6), \]
\[ (3,3),(3,6), \]
\[ (4,4), (5,5), (6,6) \} \]
(ii) Domain of \(R\)
Domain = set of first elements
\[ \boxed{ \{1,2,3,4,5,6\} } \]
(iii) Range of \(R\)
Range = set of second elements
\[ \boxed{ \{1,2,3,4,5,6\} } \]