Unequal Inequalities?

Algebra Level 2

The following are 2 statements. How many of these statements are true?

For all $x\in \mathbb R$ , either $x>0$ or $-x<0$ must be true.
If $x>0$ , then $-x< 0$ .

2 None 1

1 solution

Timothy Samson
Feb 3, 2018

For the first statement, $x = -1$ is a counterexample

For the second statement, an if statement can only be invalid if there is a case where the first part is true and the second part is false. The system of equations

$\begin{cases} x > 0 \\ -x < 0 \end{cases}$

is only true when $x > 0$ . Therefore, the second part of the if statement can only be false when $x \le 0$ . However, in the first part of the if statement we restricted $x$ to be $x > 0$ , so the second part is always true when the first part is true.

Unequal Inequalities?

1 solution

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