Mentor note: moved to homework section I'm having trouble determining if statements are combined using if/then or and operators. Take the following statements: 1) Nobody in the calculus class is smarter than everybody in the discrete math class. For 1 I'd think a proper way to term it is "For not any x's and all y's, if x students are taking calculus, and y students are taking discrete then the x students are smarter than the y students." With notation, it'd be -ExVy( C(x) and D(y) ---> S(x,y) ). (note that I use E to represent for some and V to represent for all) This answer agrees with one solutions manual but not with another. The other one says: ¬∃xC(x)∧[∀yD(y)∧S(x,y)] But wouldn't this literally mean that " no one is taking calculus and everyone is taking discrete and no calculus students are smarter than discrete math students"? That latter bit agrees with the statement, but not former, which I believe says "nobody takes calculus" 2) Everyone likes Mary, except Mary herself. I thought this looked like a fairly straightforward "and" statement. " For all x's,All people x like Mary AND x is not equal to M" Symbollically," Vx L(x,m) and m not = to x" But according to the answers manual, the answer is: Vx ( -(x=m) --> L(x,m)). Wouldn't this mean if Mary is not equal to x, then everyone likes Mary? It's somewhat similar but my answer seems a bit more straightforward. Is it possible that there are just many ways to write one statement?