Solved Examples on Transitive Property

Example 1: The weight of a novel is the same as the weight of a storybook. The storybook weighs half the weight of a textbook. If the weight of the textbook is 1.6 lb, what is the weight of the novel?

Solution:

Let the weight of the novel, storybook, and textbook be (w)_n , (w)_s , (w)_t

The weight of the novel is the same as the weight of the storybook. This indicates:

(w)_n = (w)_s (Equation 1)

The storybook weighs half the weight of the textbook. This indicates:

(w)_s = 1/2 × (w)_t (Equation 2)

Combining Equation 1 and Equation 2, we get,

(w)_n = 1/2 × (w)_t (by transitive property)

= 1/2 × 1.6

= 0.8

Therefore, the weight of the novel is 0.8 lb.

Example 2: Susan gives two hints to Mike and challenges him to find the relation between x and z. Hints : x+ y = z, z = 2y. Let’s find out how Mike can complete this task.

Solution:

Given,

x + y = z (Equation 1)

z = 2y (Equation 2)

By transitive property of equality we get,

x + y = 2y

⇒ x = 2y – y

⇒ x = y

Therefore, x = y.

Example 3: Susan offers two guidelines to Mike and challenges him to locate the relation between x and z. Hints : x+ y = z, z = 2y. Let’s find out how Mike can whole this assignment.

Solution:

Given,

x + y = z . . .(i)

z = 2y . . .(ii)

By transitive assets of equality we get,

x + y = 2y

⇒ x = 2y – y

⇒ x = y

Therefore, x = y.

Example 5: Determine the price of “a” using the transitive belongings: a+b = c and c = 3b

Solution:

Given equations:

a + b = c . . . (1)

c = 3b . . . (2)

By the use of the transitive belongings, equation (1) and (2) is written as:

a + b = 3b

⇒ a = 3b – b

⇒ a = 2b.

Therefore, the value of a is 2b.

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.