Answer:
The statement "Both of the numbers a and b cannot be even." is justified by the fact that a/b is simplified lowest terms
Step-by-step explanation:
We need to show that the √2 is an irrational number.
And from the given steps of proof stated in the question, we need to find the assumption that justifies the fact : " Both of the number a and b cannot be even".
First take the given options :
Option a : √2 is a rational number
√2 being an rational or irrational has no relation of a and b to be even or odd. So, this option is rejected.
Option B : a/b is simplified lowest terms
This shows that a and b are not even because if a and b are even then a/b can be simplified in other lowest term.
Option c : √2 is a irrational number
Similarly, By using the inverse part of Option A, option c is also rejected.
Option d : The fact that b divides a evenly
This only shows that the a is even. This does not give any idea about b is even or not. So option D is also rejected.
Option E : The fact that a and b are whole numbers
This fact does not imply that the a and b are even or odd. So option E is also rejected.
Hence, The statement "Both of the numbers a and b cannot be even." is justified by the fact that a/b is simplified lowest terms
