It is if( condition, true, false) so no parens until the end.
Also you can use or to make this simpler.
Also no quotes around field names and you are missing the final else.
For yours try
if(selected(${pretype}, 'trash') or (selected(${pretype},'none'), 'NA', if(selected(${pretype},'other'),${pretype_other}, need something in the else part here))
If these are the only 3 options then can make it even simpler
if(selected(${pretype}, 'trash') or (selected(${pretype},'none'),'NA', ${pretype_other})
Hope that helps