If \(a \in \{2,4,6,9\}\) and \(b \in \{4,6,18,27\}\), Form the Set of Ordered Pairs \((a,b)\) Such That \(a\) Divides \(b\) and \(a<b\)

Given:

\[ A=\{2,4,6,9\} \]

\[ B=\{4,6,18,27\} \]

We form ordered pairs \((a,b)\) such that:

\[ a \mid b \]

and

\[ a<b \]

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For \(a=2\):

\[ 2 \mid 4,\quad 2 \mid 6,\quad 2 \mid 18 \]

So ordered pairs are:

\[ (2,4),\ (2,6),\ (2,18) \]

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For \(a=4\):

\[ 4 \mid 4 \]

But \[ 4 \not&lt 4 \]

So no ordered pair for \(a=4\).

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For \(a=6\):

\[ 6 \mid 6,\quad 6 \mid 18 \]

But \[ 6 \not&lt 6 \]

Therefore only:

\[ (6,18) \]

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For \(a=9\):

\[ 9 \mid 18,\quad 9 \mid 27 \]

So ordered pairs are:

\[ (9,18),\ (9,27) \]

Therefore, the required set is:

\[ \boxed{\{(2,4),\ (2,6),\ (2,18),\ (6,18),\ (9,18),\ (9,27)\}} \]