91Ó°ÊÓ

Prove that the Greatest Integer Function \(f: \mathbf{R} \rightarrow \mathbf{R}\), given by \(f(x)=[x]\), is neither one-one nor onto, where \([x]\) denotes the greatest integer less than or equal to \(x\).

Give an example of a relation. Which is (i) Symmetric but neither reflexive nor transitive. (ii) Transitive but neither reflexive nor symmetric. (iii) Reflexive and symmetric but not transitive. (iv) Reflexive and transitive but not symmetric. (v) Symmetric and transitive but not reflexive.