What is Transitive Property?

The transitive property is a fundamental concept in mathematics that states that if two quantities are related to a third quantity, then all three quantities are related to each other.

In symbolic form, if a * b and b * c, then a * c

Where * represents the relation between a, b and c.

The transitive property can be applied to algebraic expressions, numbers, and various geometrical concepts. Transitive Property is a vital foundation in the process of reasoning, mathematical proofs, and applications in which building connections and dependencies is essential.

Also Check: Distributive Property

Transitive Property Definition

In formal terms, if a is related to b by some relation R, and b is related to c by the same relation R, then a is related to c by R. This can be represented symbolically as:

If aRb and bRc, then aRc.

Some examples of Transitive Property includes:

• If a is divisible by b and b is divisible by c, then a is divisible by c.
• If x belongs to set A, and A is a subset of set B, then x belongs to set B.
• If A implies B, and B implies C, then A implies C.
• If event A occurs before event B, and event B occurs before event C, then event A occurs before event C.
• If a ≡ b (mod m) and b ≡ c (mod m), then a ≡ c (mod m).

General Formula of Transitive Property

The formula for the transitive property of equality is,

If a = b, b = c, then a = c.

Here a, b, and c are three quantities of the same kind. This property holds good for real numbers.

For example, If x = m and m = 7, then we can say x = 7.

The value 7 is transferred to x because x and m are equal.

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.