If x `prop 1/y ` and y `prop 1/z ` , then x `prop `

Explanation

x `prop 1/y rArr x =k_(1)1/y` (`k_(1) ne `0= variation constant . )
`rArr y =(k_(1))/(x) ……..(1)`
Again , y `prop 1/z rArr =k_(2) 1/z` (`k_(2) ne`0= variation constant .)
`rArr (k_(1))/(x) =k_(2)1/z`
[from (1) ]
`rArr x =(k_(1))/(k_(2))z `
`rArr x=k.Z(when (k_(1))/(k_(2))kne0="variation constant")`
`rArr x prop z (because k ne0="variation constant")`
`therefore x prop z`