Please can anyone help me in this question asap please

Please can anyone help me in this question asap please Q4, Givean f : x.v€N, is not Transitive

Dear Student,
 let (a,b) belongs  to 'R' => a <= b².....(i)  9where a,b both belong to 'N' so they are +ve)

and (b,c) belongs to 'R' => b <= c²  

=> b²=> c⁴ ---(ii)  (as both b and c are +ve  so squaring can be done without changing the sign)

so from (i) and (ii),  a<= c⁴ , so (a,c) does not belong to "R" (as in that case a should be equal or less than c²)

hence the relation is not transitive

Regards