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

joaquin on July 8 at 06:39PM

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

2 Replies

Shunhe on July 10 at 06:38PM

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 at 02:17AM

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!