Which of the following statements are true and which are false? In each case give a valid reason for saying so.
$s:$ If $x$ and $y$ are integers such that $x > y,$ then $-x < -y.$
$s:$ If $x$ and $y$ are integers such that $x > y,$ then $-x < -y.$
(A) Given the inequality $x > y$.
According to the rules of inequality,if we multiply both sides of an inequality by a negative number,the direction of the inequality sign reverses.
Multiplying both sides by $-1$,we get:
$(-1) \times x < (-1) \times y$
$-x < -y$
Thus,the given statement $s$ is true.
According to the rules of inequality,if we multiply both sides of an inequality by a negative number,the direction of the inequality sign reverses.
Multiplying both sides by $-1$,we get:
$(-1) \times x < (-1) \times y$
$-x < -y$
Thus,the given statement $s$ is true.
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