Which one of the following could be the five cold medications that the study ranks, listed from first to fifth?

joaquin on July 8, 2020

Game setup diagramming and rule deduction PT 40, Section 2, Game 2

Could you please explain how is it that the ultimate deduction from the contrapositve for this rule: "H ranks better than G if both are tested" is the following: If G is 1st" then Not H. The part the puzzles me is the "if G is 1st". How can you construe the rule to mean if G is 1st, the...? Thank you in advance for your help. Joaqu´lin

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Shunhe on July 10, 2020

Hi @joaquin-acuna,

Thanks for the question! So let’s take a look at that rule again. H ranks better than G if both are tested. In other words, we have

H&G —> H>G

So let’s take the contrapositive of this sentence. Well, that gets us the following

~(H>G) —> ~(H&G)

Or in other words, since there are no ties and since ~(X&Y) = ~X v ~Y

G>H —> ~H v ~G

And translating this back into English, this means that if G ranks better than H, then both aren’t tested; either H or G is not tested.

OK, well, now let’s consider the following situation. G is 1st. Well, what does that mean? Is it possible for H to rank higher than G? No, because there are no ties, and you can’t be better than #1! So this automatically means that G>H. And so if G is first, it automatically implies that G is going to be ranked higher than H.

Hope this helps! Feel free to ask any other questions that you might have.

joaquin on July 15, 2020

thank you for the explanation, Shunhe. But, the rule deduction states that if G is first then there is NO "H" (not that G ranks better than "H") Sorry If I am missing something pretty obvious here!