Answer:
Gertrude's favorite is George Burn
What we know from the beginning:
Comedians:
- George Burn
- Jack Benny
- David Letterman
- Jerry Springfield
Lucy: Jerry Springfield is her favorite
David: Does not like David Letterman
Gertrude: Does not like David Letterman, Does not like Jack Benny anymore
Solving:
- Since we know that Jerry Springfield is Lucy's favorite, he is not longer an option. This leaves George Burn, Jack Benny, and David Letterman.
- David and Gertrude do not like David Letterman, so he must be Jose's favorite. This leaves George Burn and Jack Benny
- Gertrude does not like Jack Benny anymore, so the only one left to be her favorite is George Burn