Let’s say I was trying to prove that every time you drink Fireball, you puke. If you wanted to prove the opposite, you’d have to find a way to show that there has not been a single instance in which you both consumed Fireball and vomited. Pretty tough, right? But let’s say that instead, you just wanted to show that it’s not true that you puke EVERY time you have Fireball. You’d just have to show me a single incident in which you had Fireball and didn’t vomit.
That’s how it works with negating answer choices. A lot of people mistakenly believe that negating an answer choice means saying the opposite of that statement. That’s not the case: Instead, negating a statement simply means saying that the statement isn’t always true.
Before we get too deep into this, let’s talk about why being able to negate an answer choice should matter to you. It comes up primarily with necessary assumption questions. For instance, take this argument: “Frank is talking to Sarah at a bar. Therefore, Frank will get Sarah’s phone number.”
What assumptions are necessary for this conclusion to work? Is it necessary that Sarah has had eight shots of tequila, or that Frank is a male underwear model? Nope, although those things wouldn’t hurt. Is it necessary that Sarah has a phone? Yes, because if we negate that statement – if we say that Sarah doesn’t have a phone – the conclusion falls apart.
So that’s why we care about being able to negate statements: because it’s a good way to test whether an assumption is truly necessary. If it *is* necessary, the negation of that statement will make the conclusion no longer follow. Follow me?
Here are some handy tips for negating statements: If the statement contains the word “not,” you just take out that word. (So the negation of “Susie’s mother is not the only person who says she’s smart” would become “Susie’s mother is the only person who says she’s smart.)
How would you negate the statement “all dogs go to heaven”? We’re trying to say that it’s not always the case that all dogs are heaven-bound, so the negation would be “some dogs don’t go to heaven.” Similarly, in sentences with the word “some,” just swap it for “none” – so the negation of “some Nickelback songs are good” would be “no Nickelback songs are good.”
Lastly, what if you want to negate an entire conditional statement? For instance, take the statement “if you graduate from high school, then you know how to read.” Let’s say we want to negate that whole statement. Quite simply, we’re just trying to establish that you can have the sufficient condition (graduating from high school) without the necessary condition (knowing how to read). So the negation would be that graduating from high school does not mean you know how to read.
Negating answer choices is a powerful way to double-check your answer for necessary assumption questions, so it’s a useful skill to have. If you’re still confused, feel free to leave some examples in the comments, and we’ll help you out!