Negation of AND with TWO Variables

[patrice.antoine]

Take the infamous birds game from December 2000. One of the rules says if J and M are in, so is H.

J & M --> H

Contrapositive:

Not H ---> Not J or Not M


This negation was key to getting question #11 of the game right, but I incorrectly though that Not J or Not M means that either can be out, not necessarily both.

Is it safe to assume that when we negate "and" conditionals with two variables, the resulting "or" creates two separate conditionals, so in this instance it is:

Not H ---> Not J

AND

Not H ---> Not M

...where both triggers must result???

[noah]

Take the infamous birds game from December 2000. One of the rules says if J and M are in, so is H.

J & M --> H

Contrapositive:

Not H ---> Not J or Not M


This negation was key to getting question #11 of the game right, but I incorrectly though that Not J or Not M means that either can be out, not necessarily both.

Is it safe to assume that when we negate "and" conditionals with two variables, the resulting "or" creates two separate conditionals, so in this instance it is:

Not H ---> Not J

AND

Not H ---> Not M

...where both triggers must result???

You've actually mis-translated the rule. To paraphrase it: "If J, M, or both are in, then H are in."

This means
J --> H
M --> H

Or, J or M --> H

The "or both" is irrelevant, since either one alone triggers this (it's there just to reassure us that nothing weird happens if both are in).

In general, if we can split compound conditionals, we should.

If we did face an and trigger (and those cannot be split), such as X and Y --> Z, then the contrapositive would be:

- Z --> - X or - Y

You should look over chapter 9 in our strategy guide.

Cheers!

[moniqueposada]

I'm having a little bit of trouble with this one as well. If a rule says

J --> I or K

the contrapositive is then

-K and -I ---> -J

I am having a hard time understanding the reasoning of why the contrapositive can't be split? Or can it?