Answer:
Let us consider any two numbers 6 and 9 then we have the relation.
<em><u>Rule </u></em><em><u>1</u></em><em><u>.</u></em>
Adding 2 on both sides then;
Both are true for addition.
Thus,<u>when </u><u>equal</u><u> </u><u>number</u><u> is</u><u> </u><u>added</u><u> to</u><u> </u><u>both </u><u>sides</u><u> of</u><u> </u><u>trichotomy</u><u> </u><u>symbol,</u><u>the </u><u>symbol </u><u>remains</u><u> the</u><u> same</u><u>.</u>
<em><u>Rule </u></em><em><u>2</u></em><em><u>.</u></em>
Subtracting 2 on the both sides then,
Both are true for subtraction.
Thus,<u>when </u><u>equal</u><u> number</u><u> is</u><u> </u><u>subtracted </u><u>to </u><u>both</u><u> sides</u><u> of</u><u> trichotomy</u><u> symbol</u><u>,</u><u>the </u><u>symbol</u><u> remains</u><u> the</u><u> same</u><u>.</u>
<em><u>Rule </u></em><em><u>3</u></em><em><u>.</u></em>
Multiplying both sides by 2 then,
Both are true for multiplication by positive numbers.
But if we multiplied by -2 then there will be,
These are not true.
To be true,there must be:
Thus<u>,</u><u>when </u><u>both</u><u> sides</u><u> of</u><u> trichotomy</u><u> symbol</u><u> </u><u>are </u><u>multiplied </u><u>by</u><u> </u><u>equal</u><u> </u><u>positive</u><u> </u><u>number </u><u>then </u><u>the </u><u>symbol</u><u> </u><u>remains</u><u> the</u><u> </u><u>same.When </u><u>both </u><u>sides</u><u> of</u><u> trichotomy</u><u> </u><u>symbols </u><u>are </u><u>multiplied</u><u> </u><u>by </u><u>equal</u><u> </u><u>negative</u><u> </u><u>numbers </u><u>then </u><u>the </u><u>symbol</u><u> </u><u>changes</u><u> </u>as follows:
'<' Changes to'>' and '>' Changes to'<'.
Similarly check for division then get the same result as in multiplication.
Thus<u>,</u><u>when </u><u>both</u><u> sides</u><u> of</u><u> trichotomy</u><u> symbol</u><u> </u><u>are </u><u>divided</u><u> by</u><u> </u><u>an </u><u>equal</u><u> </u><u>positive</u><u> number</u><u>,</u><u> the</u><u> </u><u>symbol</u><u> </u><u>remains</u><u> the</u><u> </u><u>same.When </u><u>both</u><u> sides</u><u> of</u><u> trichotomy</u><u> symbol</u><u> are</u><u> divided</u><u> by</u><u> </u><u>an </u><u>equal</u><u> </u><u>negative</u><u> </u><u>number,</u><u>the </u><u>symbol </u><u>'</u><u><</u><u>'</u><u> </u><u>is </u><u>changed</u><u> to</u><u>'</u><u>></u><u>'</u><u> </u><u>or </u><u>'</u><u>></u><u>'</u><u> </u><u>is </u><u>changed</u><u> to</u><u>'</u><u><</u><u>'</u><u>.</u>