Question

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

• A. {(2,4),(2,6),(2,18),(2,54),(4,4),(6,6),(6,18),(6,54),(9,18),(9,27),(9,54)}
• B. {(2,4),(2,6),(2,18),(2,54),(4,6),(6,6),(6,18),(6,54),(9,18),(9,27),(9,54)}
• C. {(2,4),(2,6),(2,18),(2,54),(6,18),(6,54),(9,18),(9,27),(9,54)}
• D. {(2,4),(2,6),(2,18),(2,54),(4,4),(4,54),(6,18),(6,54),(9,18),(9,27),(9,54)}

Answer 1

The correct option is C {(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)}.