Relations MATHS - Relations

The relation S defined on the set R of all real number by the rule aSb iff a ≥ b is:

1. An equivalence relation.
2. Reflexive, transitive but not symmetric.
3. Symmetric, transitive but not reflexive.
4. Neither transitive nor reflexive but symmetric.

The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is:

1. Symmetric only.
2. Reflexive only.
3. An equivalence relation.
4. Transitive only.

Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if l is perpendicular to m for all l, m ∈ L. Then, R is:

1. Reflexive.
2. Symmetric.
3. Transitive.
4. None of these.

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

For the set A = {1, 2, 3}, define a relation R on the set A as follows:
R = {(1, 1), (2, 2), (3, 3), (1, 3)}
Write the ordered pairs to be added to R to make the smallest equivalence relation.

Write the smallest equivalence relation on the set A = {1, 2, 3}.

If A = {1, 2, 3, 4} define relations on A which have properties of being:
Reflexive, transitive but not symmetric.