Question

Can we generalise relation R in R defined by R = {(a,b) : a is lesser than or equal to b^n, n belongs to N} is reflexive, symmetric or transitive?

Answer 1

No, we cannot generalise relation R in R defined by R = {(a,b) : a is lesser than or equal to b^n, n belongs to N} is reflexive, symmetric or transitive.

• The relation R should obey the below properties to be defined by R = {(a,b) : a is lesser than or equal to b^n, n belongs to N}.
• Reflexive - If a ∈ R, then (a, a) ∈ R
• Symmetric - If (a, b) ∈ R, then (b, a) ∈ R
• Transitive - If (a, b) and (b, c) ∈ R, then (c, a) ∈ R
• Only the reflexive property is satisfied by the given equation, as a should be less than or equal to b^n.