Since no one lies on Sundays and A says he does so in his second statement,it means he is lying.His first statement is also therefore false.Hence A lies on Mondays,Tuesdays and Wednesdays and B lies on Thursdays,Fridays and Saturdays.Since A and B do not lie on the same day,it means B is telling the truth.Since B lies on the next day as stated by him,the day of the conversation is Wednesday.
