Answer:
Step-by-step explanation:
The aim of this question is to prove that the product of two rationals is rational.
To proof:
If [tex]\mathbf{x \ and \ y}[/tex] are arbitrary rational numbers.
Thus, going by the definition of rational, there exist integers
a, b, ≠ 0, c, and d ≠ 0 ; [tex]x = \dfrac{a}{b} \ and \ y = \dfrac{c}{d}[/tex]
Hence, [tex]xy = (\dfrac{a}{b})(\dfrac{c}{d}) = \dfrac{ac}{bd}[/tex]
Since a and c are integers, then e = ac appears to be an integer as well.
Also, provided that b and d are non-zero integers;
f =bd appears to be a non-zero integer.
Therefore, [tex]xy = \dfrac{e}{f}[/tex], and going by the definition of rational, xy is rational.
Hence, from the complete question:
The order of the statement is:
7,6,3,5,2,4
The statements that should not be used in the proof are:
1 N
8 N
9 N
10 N
11 N
