Recycling Inferences - understanding the contrapositive of a double-not arrow

[leslie7]

pg 311 of 2020 ed.

Hi just wondering if there is a reason that the full conditional isn't written out and wondering if it is correct to write it as

I->F -> G <--/-->H

Secondly,

If I ever have to understand the contrapositive of a double-not arrow (how do I understand that psychologically just from immediately looking at the linked conditional?) for example,

What would the Contrapositive look like for this ?
I->F -> G <--/-->H

Is it H -> / G - > /F -> /I ?

[KelseyWoods]

Hi Leslie!

Yes, you could link all the rules together as:

I F G H

When linking statements that use the Double Not Arrow, I find it's typically easier to just separate the Double Not Arrow into its contrapositive pair.

G H is the same thing as:
G H
H G

So you could really understand the full chain as:

I F G H

Thus, the contrapositive would be exactly as you proposed:

H G F I

Thus, based on that chain, H cannot be selected with F, G, or I. So:

H G
H F
H I

Hope this helps!

Best,
Kelsey