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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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