Transitivity of Order Relation at Algebra Den

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Home >> Order Relation >> Transitivity of Order Relation >>

Transitivity of Order Relation

Trichotomy Law Transitivity of Order Relation

To understand this, lets take an example i.e

Height of 1st pole = 8 meters.
Height of 2nd pole = 10 meters.
Height of 3rd pole = 15 meters.

Now, we can find that :-
height of 2nd pole is more than height of 1st pole i.e 10 > 8 and;
height of 3rd pole is more than height of 2d pole i.e 15 > 10.

Thus its clear also, that height of 3rd pole is greater than height of 1st pole i.e 15 > 8.

Thus, according to Transitivity of Order Relation
if 20 > 19 and 19 > 18;
then 20 > 18.

Lets understand this with the help of Algebra also:-

a > b, and there exist another natural number c;(already explained in Trichotomy Law)
which can balance the equation i.e
a = b + c .............(1)

Similarly,
b > d, and there exist another natural number e (already explained in Trichotomy Law)
which can balance the equation i.e
b = d + e..............(2)

So, by (1) and (2), we get:

a = (d + e) + c or;
a = d + (e + c)

Thus we get a > d.

Thus, according to Transitivity of Order Relation
if a > b and b > d;
then a > d.