If $AB =x$ and $x=4$, then the transitive property states
A. $A B=4$
B. $A B+x=4$
C. $A B+4=2 x$
D. $x=4$
Answer (1)
Given A B = x and x = 4 .
Apply the transitive property: If a = b and b = c , then a = c , so A B = 4 .
Compare the result with the given options.
The correct statement is A B = 4 .
Explanation
Applying the Transitive Property We are given that A B = x and x = 4 . The transitive property states that if a = b and b = c , then a = c . In this case, we can see that A B = x and x = 4 , so by the transitive property, A B = 4 .
Comparing with Given Options Now, let's compare this result with the given options:
A B = 4 : This matches our result from the transitive property.
A B + x = 4 : This is incorrect because it adds x to A B .
A B + 4 = 2 x : This is also incorrect because it adds 4 to A B and equates it to 2 x .
x = 4 : This is a given fact, but it doesn't represent the application of the transitive property in this context.
Final Answer Therefore, the correct statement that applies the transitive property is A B = 4 .
Examples
The transitive property is a fundamental concept in mathematics and logic. In real life, it can be applied in various scenarios. For example, if you know that John is the same age as Mary, and Mary is the same age as Peter, then by the transitive property, you can conclude that John is the same age as Peter. This principle helps in making logical deductions and simplifying complex relationships.
