Åk 6–9
 
English/فارسی

8.5 Transitive Law
Now we will go through the transitive law and demonstrate this with a few examples:

If Agnes is as old as Bedar and Bedar is as old as Cedar. What can you then say about Agnes and Cedars age? Are they the same age or not?

If Agnes is as old as Bedar: A = B
and Bedar is as old as Cedar: B = C
then Agnes is just as old as Cedar: A = C

We can write this as the following:

A = B = C

So:

If A = B and B = C then it follows that A = C


We will take a new example:

If 5 is less than 7: 5 < 7
and 7 is less than 12: 7 < 12
then 5 is less than 12: 5 < 12

We can write this as:

5 < 7 < 12

So:

Is 5 < 7 and 7 < 12 then it follows that 5 < 12


We can summarise both of these examples in one expression:



This is read as:
”If A is less than or equal to B, and B is less than or equal to C, then it follows that A is less than or equal to C”.