Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.

May 15, May 16, May 19 June 17, June 18 July 14, July 16 August 14, August 15, August 17

Cheryl then tells Albert only the month of her birthday and she tells Bernard only the day of her birthday.

Then Albert said: I dont know when Cheryls birthday is, but I know that Bernard does not know too.

Bernard: At first I didnt know when Cheryls birthday is, but I know now. Albert: Then I also know when Cheryls birthday is.

Waht is Cheryls birthday? Please answer this question using only propositional logic.