Question

If A={1,2,3,4.....,250} and R be the relation 'is cube of' in A,then find R as a subset of A×A. Also,find the domain and range

Answer 1

Let x and y form an ordered pair (x,y) in relation R.

Given that x is related to y , if x is cube of y

Within given limit of 250 the only perfect cubes are 1, 8, 27, 64, 125 and 216

So, R becomes

R = { (1,1) , (8,2) , (27,3) , (64,4) , (125,5) , (216,6) }


So, Domain = { 1, 8, 27, 64, 125, 216 }
And Range = { 1, 2, 3, 4, 5, 6 }