Proofs

Yesterday was my tutorial quiz day and we had to prove one statement in the quiz. Before the quiz, I was pretty confident in myself with the quiz because proving a statement is basically making assumptions, proving the consequent and then unwraping the assumptions. I was pretty stupid not to solve some extra questions and practice proving statements. The question was similar to the one on the tutorial exercise:

For all x that is in whole numbers, there exists a y in the whole numbers that makes x = 3y + 1. Then there exists a y in the whole numbers that makes x^2 = 3y + 1.

It's pretty simple right?
Square the antecedent x = 3y +1 to x^2 = 9y^2 + 6y + 1
Factor out 3 to make x^2 = 3(3y^2 +2y) + 1
Then the 3y^2 + 2y is equivalent to the consequent's y.
And then unwrap all the assumptions and the proving is done.

The question that the class received in the quiz was a little altered and when I squared the antecedent and factored out a common number, the numbers inside the bracket did not equal to the consequent's y. I was going insane on why I was not able to solve it and in the end I could not figure it out.

CSC165 is a strange course for me because half the course is more about logics and the way you think and tackle each problems in an interesting way. I was suprised that I did so poorly on my assignment #1 because it was very confusing for me but the average was 80% which is insanely high in my opinion. I need to start studying more for CSC165 and up my game in the assignments and quizzes.