NO!

 {e,a,t} = {t,e,a} = {a,t,e} = {a,e,t} = {e,t,a} = (t,a,e}}

All those are equal because they all have the EXACT same elements.
The order in which they are listed does not matter. Also, it doesn't
matter if an element is listed more than once.  {e,a,t} = {e,e,t,a,a,t,t,e}

{l,a,t,e} = {t,a,l,e} is true

However

{l,a,t,e,r} does NOT equal {l,a,t,e} 

{l,a,t,e,r} does NOT equal {t,a,l,e}

because the first set contains the element r and the second one doesn't.

However 

{l,a,t,e,r} = {a,l,t,e,r} is true.

Edwin