question_answer 5)

Check whether the relation R in R defined by R = {(a, b) : a } is reflexive, symmetric or transitive.  

Answer:

R = {(a, b) :  }          Reflexive : as       i.e.              is not reflexive.       Symmetric : As 1 < 27 for 1, 3       i.e. (1, 3)  for 1, 3       But              is not symmetric.       Transitive : As 100 < 125 and 5 < 8       i.e. 100 < 53 and 5 < 23        (100, 5)  and (5, 2)       But 100  8 i.e. 100 < 23            (100, 2)                           (100, 5) , (5, 2)          R is not transitive.       Hence R is neither reflexive nor symmetric nor transatie.