Question

WHY (CH3)3N is a base while (CF3)3N is not basic

Answer 1

Helloo!!

Fluorine is more electronegative than hydrogen as you can see in periodic table.

It polarises the covalent bond that forms between it and the carbon atom in (CF3)3N.    

hope it helps

Answer 2

in first compound ch3 is present and ch3 have +i effect it means it will give electrons to N but in 2nd compound cf3 present and cf3 have -i inductive effect which means it will take electron from N and at N electron density will be low as compared to 1st compound.
i hope this will help you