Question

Find a number that provides a counter example to show That the given statement is false.

1. For all numbers X, X > 1/x (x= )

2. For all numbers x, X + X > X (x = )

Answer 1

Answer:

the answer of the question is true

Answer 2

$X=\frac{1}{2}$ is a counterexample for statement 1.

$X=-1$ is a counterexample for statement 2.

Step-by-step explanation:

We have to give a counterexample for the statements,

1. For all numbers $X, X > \frac{1}{X}$

2. For all numbers $X, X + X > X$

For statement 1

Consider $X=\frac{1}{2}$

Then,

$\frac{1}{X}=\frac{1}{\frac{1}{2}} \\=1\times\frac{2}{1}\\=2$

Here, $\frac{1}{2}< 2$ and hence $X<\frac{1}{X}$ and therefore given statement is false.

Thus, $X=\frac{1}{2}$ is a counterexample for statement 1.

For statement 2

Consider $X=-1$

Then,

$X+X=-1+(-1)\\=-1-1\\=-2$

Here, $-2< -1$ and hence $X+X<{X}$ and therefore given statement is false.

Thus, $X=-1$ is a counterexample for statement 2.