Quantifiers Questions - - Question 1

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

Rikuto-Yamada January 30, 2022

Using the term “unless”

I would like to understand why the sentence below doesn’t follow the rule of “unless” in the sufficient and necessary condition. “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” My understanding is the, Step 1: “unless” introduces a necessary condition so the part of the sentence that follows “unless” will be the necessary condition -> So my understanding was “core of such a planetary body generates enough heat to cause volcanic action” becomes a necessary condition. However in the answer explanation, it is in the sufficient condition. Please kindly advise me on how I can understand this issue. Thank you

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Abigail January 30, 2022

Hello @rikuto-Yamada,

You are right that "unless" introduces a necessary condition, BUT you need to logically negate the sufficient condition. The Unless Rule states that "unless introduces a necessary, but you negate the sufficient." In this case, the necessary condition is “the core of such a planetary body generates enough heat to cause volcanic action (VA)” and the negated sufficient is “the surface of the body will NOT be renewed for millions of years. (NOT R)” Because this sufficient condition is already negated, its logical negation would be the positive version or “the surface of the body will be renewed for millions of years ( R).” Thus, we would diagram this as R —> VA or its contrapositive *VA —> R*. You should always right out the contrapositive. Because all conditional statements have contrapositives, each “condition” will get a chance to be the sufficient and the necessary condition, depending on whether it’s negated or not.

I hope this clarifies things. Feel free to follow up if that is still not clear.

Abigail