"Cannot"... "Unless"

cole.w.murdoch

Hey all, on PT 24, game 4, the rule reads "V cannot be prescribed unless both H and M are prescribed."
J.Y translates this to:
V -> M
V->H.
I am having trouble translating this. I know with these you take an idea, negate it, then apply the translation rule.
I keep coming up with
H & M -> V.

Hope I can get some help!

Jonathan Wang

V cannot be prescribed (no V) unless both H and M (H and M). The word "unless" is your conditional indicator here, which is group 3 - negate sufficient. Pick /V to start. V is your sufficient condition. Dump "H and M" right into the necessary, untouched. Result: V -> H and M. The 'and' is in the necessary, so you get to split the arrow. End result: V -> H and V -> M.

pchantar

The topics are: "V cannot be prescribed" and "H and M are prescribed".

It seems like you applied the group 4 rule to the stimulus, as shown by what you came up with. "Unless" falls under group 3 so you are correct that you should negate something, but the other part of the group 3 rule is that the topic you select to negate should also become the sufficient condition. In this instance, you could select the first topic matter to apply this rule to and you would get "V can be prescribed".

Doing so and putting it back into a conditional would allow it to read "If V can be prescribed, then H and M are prescribed", which is equivalent to V -> H&M, also the equivalent of V -> H and V -> M combined. Seems like JY just chose the split up the necessary condition into two conditionals.

cole.w.murdoch

Thanks to you both. I appreciate it!

kraft.phillip

The cool thing about unless is that you don't have to figure out which is the Necessary or the sufficient condition. You just need to pick one of the conditions, negate it, and put the other one as the necessary condition untouched. With your example above, "V cannot be prescribed unless both H and M are prescribed," pick either "~V" or H and M, negate it, and throw the other into the necessary spot. if you do both, you'll see that you get contrapositives.

~V becomes V, into the Sufficient:

V->

H and M into the Necessary, untouched, so:

V->H and M

Alternately,

H and M becomes ~H or ~M, into the Sufficient:

~H or ~M->

~V into the Necessary, untouched, so:

~H or ~M->~V

V-> H and M = ~H or ~M->~V via contrapositive.