Question about contrapositives and splitting compound conditionals. Forum

[JCDante]

Going through the Trainer: just got a couple questions.

1.) Why does "or" turn into "and" when you reverse and negate during a contrapositive (and vice versa)? I understand that this is a method to take advantage of, but I do no understand the abstract reasoning behind it.

2.) If I understand correctly, when you have a trigger with "and", you cannot split it up, correct?

For example: If not H ----> J or L
If not J & not L ----> H

This cannot be split because if not J & not L are tied together. But say this was:

If not J or not L ----> H

then it could be split into

Not J ----> H
Not L ----> H

[DrYamata]

Going through the Trainer: just got a couple questions.

1.) Why does "or" turn into "and" when you reverse and negate during a contrapositive (and vice versa)? I understand that this is a method to take advantage of, but I do no understand the abstract reasoning behind it.

2.) If I understand correctly, when you have a trigger with "and", you cannot split it up, correct?

For example: If not H ----> J or L
If not J & not L ----> H

This cannot be split because if not J & not L are tied together. But say this was:

If not J or not L ----> H

then it could be split into

Not J ----> H
Not L ----> H

Just think about it in concrete terms real quick.. it always helps to bring logic down to the real world to understand it.. just make sure to be able to take it back up into abstraction

1. If I said "There are apples or oranges." It means there is either fruit, or both fruits (unless it's an exclusive or.) To say that it is not the case that there are apples, oranges, or both, you have to say "not apples AND not oranges" which is logically equivalent to "not (apples or oranges)" I suggest just drilling the hell out of demorgan's laws.. just memorize it. It's only a few logical operators and you need to be able to whip it out on test day.

2. Correct. "AND" sufficient conditions must occur together in order to trigger the necessary.

[JCDante]

Thank you so much! That example really cleared things up for me.