Data Validity feature

I need help in data validity feature. If value of A1 is X, then B1 should display a value; if value of A1 is Y, then B1 should display a different value. For all other values, B1 should display as N/A. Please help.

This doesn’t look as if it is actually about Data > Validity.
=IF(A1="X";Xvalue;IF(A1="Y";Yvalue;NA())) in cell B1 should do.

If you actually want to get different “DropDownLists” for B1 depending on the content of A1:
Put the alternative lists into different cell ranges, choose the option Cell range in the validity dialogue, and enter into the range field a formula like
IF(A1="X";$Sheet1.$A$11:$A$20;IF(A1="Y";$Sheet1.if$A$21:$A$30;NA())).
Data > Validity accepts calculated ranges.