Give an example of a relation which is transitive but neither reflexive nor symmetric.

Give an example of a relation which is symmetric but neither reflexive nor transitive.

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 symmetric and transitive but not reflexive.

Give an example of a relation which is reflexive and transitive but not symmetric.

Give an example of a relation which is reflexive and symmetric but not transitive.

Prove that the relation "less than" in the set of natural number is transitive but not reflexive and symmetric.

Prove that the relation "less than" in the set of natural number is transitive but not reflexive and symmetric.

(i) Show that in the set of positive integer, the relation ' greater than ' is transitive but it is not reflexive or symmetric.

What are rational numbers? Give four examples of each of positive rationals and negative rationals. Give an example of a rational number which is neither positive nor negative.

Give an example of a geometrical figure which has neither a line of symmetry nor a rotational symmetry.