Show that the hypotheses Solution first look at the first statment, there are 2 choices. if you take the first part of the statment as true then you left your notes in the library. given the or statment only one part of the statment can be true so you did not finish the rough draft. following the logic into the next statment, if you left you notes in the library then the first part of the second statment is false so the you must have revised the bibliography. now let\'s go back and choose the second part of the first statment to be true. now you did finish our rough draft so you did not leave your notes in the library which follows from the second statment that you did not revise the bibliography. let p = I left my notes in the library let ~p = I did not leave my notes in the library let q = I finished the rough draft of the paper let r = I revised the bibliography p or q implies if p then ~q and if ~p then q ~p or r implies if ~p then ~r and if p then r so: if p then ~q and r or: if ~p then q and ~r I hope this made it clearer for you..