91Ó°ÊÓ

The properties of inequality are also known as axioms of inequality.

The addition property of inequality is:

For any real number $a$, $b$ and $c$.

If $a<b$, then $a+c<b+c$ and

If $a>b$, then $a+c>b+c$.

The subtraction property of inequality is:

For any real number $a$, $b$ and $c$.

If $a<b$, then $a-c<b-c$ and

If $a>b$, then $a-c>b-c$.

The multiplication property of inequality is:

For any real number $a$, b and c

Where, c is negative:

If $a<b$, then $ac>bc$and

If $a>b$, then $ac<bc$.

Where, c is positive:

If $a<b$, then $ac<bc$ and

If $a>b$, then $ac>bc$.

From the given, $a<b$and $c<0$that is c is negative.

Then using the multiplication property, $ac>bc$].

Using addition property, $a+c<b+c$and

Using subtraction property, $a-c<b-c$

For $a<b$ and $c<0$ , the possibilities are $ac>bc$, $a+c<b+c$ and $a-c<b-c$ .

Then statement I that is $ac>bc$holds.

Statement II that is $a+c<b+c$also holds.

But Statement III that is $a-c>b-c$ does not hold.

As I and II holds, then,

Option A that is I only is not true.

Option B that is II only is not true.

Option C that is III only is not true.

Option D that is I and II only is true.

Option E that is I, II and III is not true.

Therefore, the options that is true is option D (that is I and II only).