Ermahgerd.
So far into the course, memorizing the symbols is pretty easy but knowing when to use them is a bit difficult. When I first looked at the tutorial handout for this week, I had no idea where to start. I was so confused with the structure of how we write an implication because I did not know what form was considered bad or good. It was so hard figuring out what to do because I did not know how the symbolic grammar worked at first, but referring to previous class examples and debating with other peers, for hours, helped out a lot. I'm hoping that the course exercises Prof. Heap posted on the class site will help.
So far into the course, memorizing the symbols is pretty easy but knowing when to use them is a bit difficult. When I first looked at the tutorial handout for this week, I had no idea where to start. I was so confused with the structure of how we write an implication because I did not know what form was considered bad or good. It was so hard figuring out what to do because I did not know how the symbolic grammar worked at first, but referring to previous class examples and debating with other peers, for hours, helped out a lot. I'm hoping that the course exercises Prof. Heap posted on the class site will help.
At some point in the
week I had the implication symbol (=>) and the comma(,) mixed up. I didn't
know when which was appropriate to use. I figured that I mixed the usage of the
comma in logic with its typical usage in English, where in English, we can imply
if…, then… using
the comma for emphasis on an implied fact, but the comma in logic is used
purely for separation in logic.
Being super literal
in CSC 165 is key :P.
On the other hand, what I am still stuck on is the
concept of the contrapositive and negation in terms of what they are meant to
do in theory. All I that I know of for now is how they work, i.e. a negation is the opposite of
a logical piece or variable and a contrapositive is formed by reversing
an implication and making both sides P and Q 'opposited', but what exactly is
the significance of a contrapositive versus negation and their differences?
Say you have to prove that P => Q, but that it's really difficult to do so. Sometimes it might be very easy to show that ~Q => ~P (contrapositive) though! And you've learnt in this course that a statement and its contrapositive are equivalent, so proving ~Q => ~P also proves that P => Q! (It's called 'Proof by Contrapositive')
ReplyDeleteThe significance of the negation is... well... that it's the opposite. Say you want to prove that something is NOT true, that is the same is proving that the negation IS true. Think about it!