  The position and momentum space information entropies of weakly interacting
trapped atomic Bose-Einstein condensates and spin-polarized trapped atomic
Fermi gases at absolute zero temperature are evaluated. We find that sum of the
position and momentum space information entropies of these quantum systems
contain $N$ atoms confined in a $D(\le 3)$-dimensional harmonic trap has a
universal form as $ S_t^{(D)} = N(a D - b \ln N) $, where $a \simeq 2.332$ and
$b = 2$ for interacting bosonic systems and $a \simeq 1.982$ and $b = 1$ for
ideal fermionic systems. These results obey the entropic uncertainty relation
given by the Beckner, Bialynicki-Birula and Myceilski.
