Unless Clause Negation or "If not"?

[andrewgong01]

This is really confusing me from Prep24 G4 when dealing with an unless. I always thought "unless" statements were treated by using the "If not" rule to replace unless; however, in this case I am really confused :

V can not be in unless both H and M are in. Using the unless rule, it is If neither H nor M are in then V is not in. However, the official answer is that this statements means V --> H and M in. This means that the unless statement of H and M was translated such that not only did we add an "if not" but also changed the "and/nor" to an either/or? For unless statements, is it not really accurate then to say it is simply add an "if not" ; rather we need to negate the entire statement so that the and/nor or diction switches too?

[ohthatpatrick]

Applying the "if not" rule is same idea of negation we use when we write a contrapositive.

V can not be in unless both H and M are in = "If it's not the case that [both H and M are in] --> V can not be in"

Do both H and M have to be out to trigger the left side?

No. As long as either one of them is out, "it is not the case that "both H and M are in".

If you prefer mathematical visuals,
~(H and M) --> ~V

When you distribute that ~ through the parenthesis,
H flips to ~H
AND flips to OR
M flips to ~M

~H or ~M --> ~V

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If you ever see an unless statement and the unless is attached to a more complex idea than the other idea in the sentence, feel free to just mentally move the unless.

It doesn't make any difference which idea in the sentence "unless" is attached to. You get the same conditional rule either way.

Bob will come unless Maria makes stew = Unless Bob comes, Maria will make stew

Those both give you the same rule:
~M stew --> B comes
~B comes --> M stew

So if you see "V can not be in unless both H and M are in" and you don't trust yourself to 'if not' the 2nd idea correctly, then just pretend the sentence said "Unless V is not in, then both H and M are in"

You'll get
V is in --> H and M are in
~H or ~M --> ~V