If a ∈ {2, 4, 6, 9} and b ∈ {4, 6, 18, 27}, then form the set of all ordered pairs (a, b) such that a divides b and a

Question

If a ∈ {2, 4, 6, 9} and b ∈ {4, 6, 18, 27}, then form the set of all ordered pairs (a, b) such that a divides b and a<b.

Philoid · Accepted Answer

given that a ∈ {2, 4, 6, 9} and b ∈{4, 6, 18, 27}.

To find: ordered pairs (a, b) such that a divides b and a

Here,

2 divides 4, 6, 18 and is also less than all of them

4 divides 4 and is also less than none of them

6 divides 6, 18 and is less than 18 only

9 divides 18, 27 and is less than all of them

Therefore, ordered pairs (a, b) are (2, 4), (2, 6), (2, 18),

(6, 18), (9, 18) and (9, 27)