Pinocchio’s Hats

This problem in logic from Presh Talwalkar recalled an article I wrote a while ago but did not publish.  So I thought I would post it as part of the solution.

“Assume that both of the following sentences are true:

  1. Pinocchio always lies;
  2. Pinocchio says, “All my hats are green.”

We can conclude from these two sentences that:

  • (A) Pinocchio has at least one hat.
  • (B) Pinocchio has only one green hat.
  • (C) Pinocchio has no hats.
  • (D) Pinocchio has at least one green hat.
  • (E) Pinocchio has no green hats.”

Actually, the question is which, none or more, of statements (A) – (E) follow from the two sentences?

See Pinocchio’s Hats

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