Is unique index always used if query is on first constituent column ?

Hi,

suppose we have 2 columns a and b . we need to query by a and sometimes
by b for data consistency UNIQUE(a,b) also needs to be there. we create
indexes below:

create unique index ab on t(a,b);
create index b on t(b);

it has been observed that index ab is used while querying
for a , can we always avoid creating the extra index on a ie,
create index a on t(a); (does other databases also behave
similar?)

Regds
mallah.