I was looking at the following question:
[which is the stronger logic statement](https://math.stackexchange.com/questions/1488510/which-is-the-stronger-logic-statement)

The original poster provides two statements with the only difference being the order of the quantifiers as follows:

$\forall a \exists b \forall c \; Sport(a,b,c)$ (1)

& 

$\forall a \forall c \exists b \;Sport(a,b,c)$ (2)
where a,b represent people.

My question is, why exactly is there a difference in the "strength" of a statement due to the order of the quantifiers? I have read the answer on the aforementioned question, but I am looking for something which is a bit more concrete. 

My interpretation of (1) in English is as follows:

> 
> For each person $a$, there is a sport $b$, which is shared by every other person $c$
> 
> 
> 

Similarly, my interpretation of (2) in English is as follows:

> 
> For every person $a$ and $c$, there is a sport $b$ which they share
> 
> 
> 

Are these two statements not equivalent? Could someone prove this?