Why does JY write not-both rules asymmetrically?

brennan

In the games videos, when JY sees the rule "if P, then not Q", he writes:

P -> Q

But when he sees "if Q, then not P" he writes:

Q -> P

But these mean exactly the same thing. Why write it one way but not the other?

It seems to me that something like P <-|-> Q would express the symmetry better, and visually indicate to the reader than P and Q are "equal" with respect to their relationship under this rule.

draj0623

I think in the LG curriculum he acknowledges that some students use <--|--> or A <----->/B to describe this relationship. He basically recommended using the convention that works best for you and maintaining consistency to avoid confusion. I personally use the standard not both for linking up different rules into bigger conditional chains and I'll sometimes use <---|--> if it's a grouping game with many groups and 2 items hate each other. I think it's visually helpful but maybe not as helpful as putting both items in a box and crossing it out. Just be consistent in the way you use them and develop that comfort level and trust in yourself.

draj0623

Also, I think maybe JY doesn't write out the contrapositive form of every rule because this translation needs to be second nature.

LSATShinobi

@draj0623 said:
Also, I think maybe JY doesn't write out the contrapositive form of every rule because this translation needs to be second nature.

Yeah usually writing it one way implies the contrapositive, so it need not be written as long as it is kept in mind.

Sami

@brennan said:
t seems to me that something like P <-|-> Q would express the symmetry better

I think thats fine as long as you understand the relationship. The trick is in conditional chains when you have multiple things linking with Q and others with P. Then its easier to see the relationship and other inferences if you write:
Q----> P

Cant Get Right

@brennan said:
P <-|-> Q

Visually, I don't like seeing an arrow run from the necessary back to the sufficient. That represents a false relationship because the sufficient term is unaffected by the satisfaction of the necessary. The absence of one does not guarantee the presence of the other, as a biconditional arrow would indicate. As others have said, conditional logic should be so second nature that seeing the contrapositive is natural. The standard representation does express the symmetry if you are comfortable with the language. Like @Sami suggested, it's also a deviation from our standard notation which makes it awkward within context. The important thing is definitely that you understand what it all means, but I think the representation JY uses is a lot better once you're used to it.