is this a practical way of proving math theorems? i asked because when i tried, it seemed difficult for me to decide as to how exactly i should translate theorems and given statements into logical forms and since there are so many different ways, i do not know which one is correct. For example, I was asked to prove the statement "If 0<a<b, then a^2 < b^2" I: 0<a<b A: multiply the given inequality by a B: multiply the given inequality by b C: 0 < a^2 < ab D: 0 < ab < b^2 E: a^2 < b^2 (I ^ A) --> C (I ^ B) --> D (C ^ D) --> E therefore, (I ^ E) --> Q am i doing this right? and what i really want to know is how do i do it the most efficient way? or is proving math theorems simply a different animal compared to symbolic logic proofs? is practicing with symbolic logic proofs mainly a way of getting my brain to think in a certain way? thank you all.