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Subsection 7.3.6 We’re Often Sloppy

Sometimes the problem is even worse than just omission. We’re often sloppy and we count on our listeners/readers to figure out what we really must have meant.

Look at the sign shown below on the right. To its left is a picture that makes it clear that the sign doesn’t mean what it says. It probably is meant to say something like, “Must be at least 42 tall to climb.

Exercises Exercises

Exercise Group.

Consider this airport sign. Taken literally, it says that if you’re 12 and under, the rule applies to you. Let’s try to figure out whether that’s what it really means.

Part 1.

Reese is 10. Is this claim true or false:

age(Reese) = 12 ∧ age(Reese) < 12.

  1. True

  2. False

Answer.

Correct answer is B.

Part 2.

Reese is 12. Is this claim true or false:

age(Reese) = 12 ∧ age(Reese) < 12.

  1. True

  2. False

Answer.

Correct answer is B.

Part 3.

Reese is 15. Is this claim true or false:

age(Reese) = 12 ∧ age(Reese) < 12.

  1. True

  2. False

Answer.

Correct answer is B.

Solution.

Explanation: No number can be both equal to 12 and less than 12. So, as we’ve just seen, this sign applies to no one.

This sign really means, “If you’re 12 OR under …”

This particular confusion happens a lot. If we’d rephrased the condition in terms of sets, we could correctly have used “and”:

Kids who are 12 AND kids who are under 12 can keep their shoes on.