Transitive Property

What is transitivity?

Transitivity is a property that describes a relationship or operation that can be extended from one element to another through a common intermediary.

Does transitivity holds for equality?

Yes, transitivity holds for equality as a = b, b = c ⇒ a = c.

Does transitivity holds for Inequality?

Yes, transitivity holds for equality as a < b, b < c ⇒ a < c or a > b, b > c ⇒ a > c.

What is Transitive Relation?

A relation R on a set A is transitive if, for all a,b,c in A, if aRb and bRc, then aRc.

What is an example of a transitive relation?

An example of a transitive relation is the “less than” (<) relation on the set of real numbers.

How to use transitive property?

To use transitive property we need to see three elements are related to each other with same relation

What is difference between transitive property of inequality and congruence?

Transitive property of inequality is used particularly for establishing relation between three elements while transitive property of congruence relates three geometric shapes

Transitive Property is a fundamental concept used when dealing with three or more quantities of the same kind related by some rule. Three elements are said to satisfy transitive property if a is related to the b by a certain rule, and the b is related to the c by the same rule, then we can definitely say that the a is related to the c by the same rule.

In simple words, if a implies b and b implies c, then a implies c. In this article, we will discuss all the topics related to Transitive Property including its definition, examples and various solved examples as well.