# Consumer: A new law requires all cigarette packaging to display health warnings, disturbing pictures of smoking-relat...

maonuo on January 9, 2020

how to negate answer D?

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shunhe on January 13, 2020

Hi @Maonuo,

Thanks for the question! (D) is tricky argument to negate because weâ€™re negating a conditional statement. First, letâ€™s diagram out (D). Itâ€™s an unless statement, and recall that we can diagram â€œX unless Yâ€ as ~Yâ€”>X. So, applying this to (D), we have

PFLP = people frequently look at the packaging (when taking out cigarettes)
NPASMHP = new packaging affects the smoking habits of people

~PFLP â€”> ~NPASMHP (where â€œ~â€ is shorthand for not)

Now, Iâ€™m going to walk through the formal logic of how to negate the sentence first. We can express pâ€”>q as ~p v q. This is because either p or ~p happens. If ~p happens, obviously, we can conclude ~p. If p happens, we can conclude q by the conditional. Thus, if we know that pâ€”>q, we know that either ~p, or q.

Now we can negate this statement, which gets us p & ~q. This is the negation of the conditional. Applying this to our example, the negation is ~PFLP & NPASMHP.

Letâ€™s walk through this in English. Letâ€™s take an example to understand this. Letâ€™s say we have the following: if I eat this chicken sandwich, I will be full. Whatâ€™s the negation of this? Something thatâ€™s true when this is false and vice versa is the following statement: I ate this chicken sandwich, and I am not full. That shows that the conditional isnâ€™t true, since the sufficient condition happened but the necessary condition didnâ€™t. This, in our example, the negation of (D) occurs when people arenâ€™t frequently looking at the packaging when taking out cigarettes, but the packaging is still affecting the smoking habits of people. And this makes sense. How do we negate a sentence that tells us that X wonâ€™t happen, unless Y happens? Show that X did happen, even though Y didnâ€™t happen. Hope this helps! Feel free to ask any other questions that you might have.