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

Important Questions on Relation and Function
Give an example of a relation which is reflexive, transitive but not symmetric

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

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

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

Give an example of a relation which is an empty relation.

Give an example of a relation which is a universal relation.

Let be a relation on , If is symmetric then . If it is also transitive then . So whenever a relation is symmetric and transitive then it is also reflexive. What is wrong in this argument?

Suppose a box contains a set of balls (denoted by ) of four different colours (may have different sizes), viz. red, blue, green and yellow. Show that a relation defined on as is an equivalence relation. How many equivalence classes can you find with respect to ?
[Note: On any set a relation satisfy the same property is an equivalence relation. As far as the property is concerned, elements and are deemed equivalent. For different we get different equivalence relations on ]
