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

shunhe on January 13, 2020

Hi @Maonuo,

Thanks for the question! (D) is tricky argument to negate because we’re negating a conditional statement. First, let’s diagram out (D). It’s an unless statement, and recall that we can diagram “X unless Y” as ~Y—>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 —> ~NPASMHP (where “~” is shorthand for not)

Now, I’m going to walk through the formal logic of how to negate the sentence first. We can express p—>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 p—>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.

Let’s walk through this in English. Let’s take an example to understand this. Let’s say we have the following: if I eat this chicken sandwich, I will be full. What’s the negation of this? Something that’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 isn’t true, since the sufficient condition happened but the necessary condition didn’t. This, in our example, the negation of (D) occurs when people aren’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 won’t happen, unless Y happens? Show that X did happen, even though Y didn’t happen. Hope this helps! Feel free to ask any other questions that you might have.