If A={4, 6, 10, 12} and R is a relation defined on A as two elements are related iff they have exactly one common factor the relation r is
Answer (1)
2nd Oct, 2018
Here A={4,6,10,12}
so A*A={(4,4),(4,6),(4,10),(4,12),(6,4),(6,6),(6,10),(6,12),(10,4),(10,6),(10,10),(10,12),(12,4),(12,6),(12,10),(12,12)}
so the relation R # A*A
where # indicates subset
R={(x,y) s.t. x and y have only one common factor and (x,y) # A*A}
Find the Elements in A*A such that they have only one common factor.
We see that (4,6),(4,10),(6,4),(6,10),(10,4),(10,6),(10,12),(12,10) are the elements which have only one common factor EXCEPT 1
But Note that 1 IS ALSO A COMMON FACTOR, SO ALL THE ELEMENTS OF A*A HAS MORE THAN ONE COMMON FACTOR HENCE THE RELATION IS VOID SET.
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