Call the statements A-G.
B and F both say that today is wednesday but they cannot both be right at the same time.
E implies D, if E were true then D would also be true so this cannot be the case
Same thing for G in place of E above.
The question doesn't have a solution. If today is monday then Alexis is right and everyone else is wrong, if today is tuesday then Bandy is right and everyone else is wrong, if today is thursday or saturday then Dilbert is right and everyone else is wrong.