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
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.
Table of Content
- What is Transitive Property?
- Examples of Transitive Properties
- Transitive Property of Equality
- Transitive Property of Inequality
- Transitive Property of Congruence
- Transitive Property of Angles