help on nested IF formula with several conditions

Try

=IF(COUNTIFS($A$1:$A$10,A1)=COUNTIFS($A$1:$A$10,A1,$B$1:$B$10,"<>"),"Closed",IF(COUNTIFS($A$1:$A$10,A1)<>COUNTIFS($B$1:$B$10,"<>"),"Open",IF(B1<>"","Closed","Open")))