Remember truth tables? *If p, then q. Inverse, Converse, Contrapositive, etc. *First, a quick review. Take the true statement “If you paint, then you’re an artist”

**Inverse**: “If you don’t paint, then you’re not an artist.”

*(False. What if you just sculpt?)***Converse**: ”If you’re an artist, then you paint”

*(False. What if you just sculpt?)***Contrapositive**: “If you’re not an artist, then you don’t paint.”

*(Ok, true, because if you did paint, you’d be an artist)*

The point is that only the contrapositive is logically equivalent to the original statement.

Now, take a look at the statement “If you eat fat, then you’ll increase the odds of cardiovascular disease.” What’s the inverse? ”If you **don’t **eat fat, then you **will not** increase odds of cardiovascular disease.” Well, as you know, the *inverse* is not logically equivalent to the original statement, and therefore can’t be *assumed* as true. In this example, limiting fat can lead to eating more carbohydrates (while keeping protein intake constant), which may be linked to cardiovascular disease

** **** **** ****Watch 29:15 to 31:23 for this example of the incorrectly assuming the inverse is also necessarily true.**

By the way, this lecture was the subject of a recent NYMag article titled **Is Sugar Toxic?**