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Question

Given : x {2,4,6,9} and y {4,6,18,27,54}.
Form all ordered pairs (x,y) such that x is a factor of y and x<y.
  1. {(2,4),(2,6),(2,18),(2,54),(4,4),(4,54),(6,18),(6,54),(9,18),(9,27),(9,54)}
  2. {(2,4),(2,6),(2,18),(2,54),(4,6),(6,6),(6,18),(6,54),(9,18),(9,27),(9,54)}
  3. {(2,4),(2,6),(2,18),(2,54),(4,4),(6,6),(6,18),(6,54),(9,18),(9,27),(9,54)}
  4. {(2,4),(2,6),(2,18),(2,54),(6,18),(6,54),(9,18),(9,27),(9,54)}


Solution

The correct option is D {(2,4),(2,6),(2,18),(2,54),(6,18),(6,54),(9,18),(9,27),(9,54)}
2 is a factor of 4, 6, 18 and 54
4 is a factor of 4 but x < y is not satisfied.
6 is a factor of 6, 18 and 54 but we consider only 18 and 54.
9 is a factor of 18,27 and 54.
Hence the ordered pairs are : {(2,4),(2,6),(2,18),(2,54),(6,18),(6,54),(9,18),(9,27),(9,54)}.

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