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Home >> Order Relation >> Trichotomy Law >>

Trichotomy Law

 Trichotomy Law Transitivity of Order Relation

According to Trichotomy Law :-

When we have two Naturals Numbers a and b, then only one of the following possibilities can be true

1) a = b

2) a > b

3) a < b

This Law further elaborates that:

If a > b, ---------------(Statement 1)

then there can exist another natural number (c) which can balance the equation i.e.

a = b + c---------------(statement 2)

Now, from statement (1) and (2), we get:
a > c

E.g. There are two natural numbers i.e. 20 and 25
We can observe that
25 > 20

Now, in order to equate it we add 5 to 20 and we get the following equation:
25 = 20 + 5

And this further shows that:
25 > 5

Hence, Trichotomy Law says that:
If a > b
then a = b + c
and a > c

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