The relation `S` defined on the set `R` of all real number by the rule `a\ S b` iff `ageqb` is (a) equivalence relation (b)reflexive, transitive but not symmetric (c)symmetric, transitive but not reflexive (d) neither transitive nor reflexive but symmetric

Let R be a relation defined by R={(a, b): a >= b, a, b in RR} . The relation R is (a) reflexive, symmetric and transitive (b) reflexive, transitive but not symmetric (c) symmetric, transitive but not reflexive (d) neither transitive nor reflexive but symmetric

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

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

The given relation is defined on the set of real numbers. a R b iff |a| = |b| . Find whether these relations are reflexive, symmetric or transitive.

The following relation is defined on the set of real number: a R biff1+a b >0 Find whether this relation is reflexive, symmetric or transitive.

If A = {1, 2, 3, 4}, define relations on A which have properties of being (i) reflexive, transitive but not symmetric. (ii) symmetric but neither reflexive nor transitive. (iii) reflexive, symmetric and transitive.

Every relation which is symmetric and transitive is also reflexive.

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.

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