Large inequalities in wealth always threaten the viability of true democracy, since wealth is the basis of political ...

shunhe May 30, 2020

Hi @CateChipman,

Thanks for the question! So you can definitely make connections via the transitive property between contrapositive statements and an original conditional (which I assume is what you mean by “positive” statement? Is this terminology that we use?). I wouldn’t call it “random” linking, though, there’s a well-defined methodology.

You can link together chains via the transitive property as long as the same term is in the sufficient condition of one and the necessary condition of the other (or on the left side of one statement and the right side of another), since the transitive property is really just a shortcut way of writing things down. For example, let’s say we’re given

A—>B
~C—>~B

What we can do here is take the contrapositive of the second statement (which is logically equivalent to the original statement) to get

A—>B
B—>C

And we can then link these two statements together to get

A—>B—>C

And then we can use the transitive property to just write

A—>C

To make this more concrete, here’s an example.

If it is hot, I will eat ice cream.
If I don’t eat sweet cream ice cream, I will not eat ice cream.

So we take the contrapositive of the second statement:

If it is hot, I will eat ice cream.
If I eat ice cream, then I will eat sweet cream ice cream.

Now, intuitively, in your head, you already know this means if it’s hot, I’ll be eating sweet cream ice cream. Because if it’s hot, I’ll eat ice cream, and if I eat ice cream, it’s sweet cream ice cream. That’s all we’re representing when we’re using the transitive property.

Hot —> Ice cream —> Sweet cream ice cream

Or, in other words,

Hot —> Sweet cream ice cream

And that’s how we link statements together. Doesn’t matter if it’s a contrapositive or the original conditional; as long as the requirements above are met, we can link them together in that way.

Hope this helps! Feel free to ask any other questions that you might have.

ohanamgt June 17, 2020

Is this diagram:
PR. TD ---> not W
W ---> PP
C: TD ---> W
?