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"You cannot ride the roller coaster if you are under $4$ ft tall, unless you are older than $16$ years old."

$q$: ride the coaster

$r$: under $4$ft tall

$s$: older than $16$

It was my understanding that "unless" translates to "if not" therefore I came up with: $$\neg s \to (r \to \neg q).$$

However, the book gives this as the answer:

$$(r \land \neg s) \to \neg q.$$

Which makes sense, however I don't see where the "and" comes from. Does "unless" mean something different in this context?

thanasissdr
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Anon
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1 Answers1

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You are right, and so is the book.   The answers are equivalent.

$$\neg s \to (r \to \neg q) \iff (\neg s\wedge r)\to \neg q$$

In either case the only way to guarantee $\neg q$ holds is if both $\neg s$ and $r$ hold.

This is called the rule of Exportation.

$$P\to (Q\to R) \dashv\vdash (P\wedge Q)\to R$$

Graham Kemp
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