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I am trying to translate an English sentence to the logical expression:

You cannot ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old.

$q$: You can ride the roller coaster

$r$: You are under 4 feet tall

$s$: You are older than 16 years old

I am confused about the way books answers this question:

Book's answer:

$$(r ∧ ¬s) \rightarrow ¬q.$$

My answer:

$$¬q \rightarrow (¬s \rightarrow r) $$

These are not equivalent statements. So which interpretation is correct?

Cody
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  • @quasi done my bad – Cody Aug 12 '20 at 05:39
  • Your statement says "if you can not ride the roller coast than (if you aren't older than sixteen then you are under sixteen". What if you can't ride the roller coaster because you are dead. Or because you are on the moon. Or because it is against your religion. Or because it is closed for repairs. The statement doesn't say those are the only reasons you can't ride the roller coaster. It just says if those conditions are true you can't ride the roller coaster. – fleablood Aug 12 '20 at 06:18

1 Answers1

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The book's answer is correct.

Rewriting the book's answer back to English would give

"If you are under $4$ feet tall and younger than $16$, then you can't ride the roller coaster."

The given statement gives a prerequisite condition which, if not met, bars someone from riding the roller coaster. It's not an "if-and-only-if" type statement.

Your version has the form "If you can't ride the roller coaster, then . . .", but for all we know, there may be other conditions as well (e.g., "You can't ride if you don't have a ticket.").

quasi
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