Planetary bodies differ from one another in their composition, but most of those in the Solar System have solid surfa...

shunhe January 8, 2021

Hi @Francesca,

Thanks for the question! So first, remember that “X unless Y” can be diagrammed in two ways (since they’re contrapositives):

~Y —> X

~X —> Y

You’re probably more used to the second way, since we teach you that “unless” introduces the necessary, and you put the rest in the sufficient and negate it, so I’ll complete the rest of the diagram using this method.

Here, we have the following statement: “Unless the core of such a planetary body generates enough heat to cause volcanic action, the surface of the body will not be renewed for millions of years.”

So this is phrased “Unless Y, X.” Which is fine. Remember, unless introduces the necessary. So we’ll have

[something] —> Core generates enough heat to cause volcanic action

Now for the sufficient part. We take what’s left and negate it.

~ (surface of the body won’t be renewed for millions of years) —> Core generates enough heat to cause volcanic action

Notice, however, that we have a negation and a “won’t.” That’s a double negative and kind of ugly and hard to work with. Remember, two negatives cancel each other out (like multiplying negative numbers), so we can just write

Surface of the body renewed within millions of years —> Core generates enough heat to cause volcanic action

And that’s the final diagram!

Hope this helps! Feel free to ask any other questions that you might have.