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.

Give an example of a relation. Which is(i) Symmetric but neither refle

1.	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.
Answer» (i) Relation that is symmetric but neither reflexive nor transitive. `R = {(x,y),(y,x)}` (ii) Realtion that is transitive but neither reflexive nor symmetric. `R = {(x,y),(y,z),(x,z)}` (iii) Relation that is reflexive and symmetric but not transitive. `R = {(x,x),(y,y),(x,y),(y,x)}` (iv) Relation that is reflexive and transitive but not symmetric. `R = {(x,x),(y,y),(z,z),(x,y),(y,z),(x,z)}` (v) Relation that is symmetric and transitive but not reflexive. `R = {(x,y),(y,x),(y,z),(z,y),(x,z),(z,x)}`