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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. |
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