High School

What is a logical translation of "there is only one animal that scares Mr. Smith and does not scare Mrs. Smith"?

Answer :

Final answer:

The logic translation of the given statement indicates that there is one animal that scares Mr. Smith and doesn't scare Mrs. Smith, while all other animals that scare Mr. Smith also scare Mrs. Smith.

Explanation:

The logic translation of the given statement is:

Let's say that 'x' is the animal that scares Mr. Smith and doesn't scare Mrs. Smith.

The logical expression for the given statement would be:

∃x [(Animal(x) ∧ Scares(x, Mr. Smith)) ∧ ¬Scares(x, Mrs. Smith)] ∧ ∀y [(Animal(y) ∧ Scares(y, Mr. Smith) ∧ ¬(x=y)) → (Scares(y, Mrs. Smith))]

This translation states that there exists an animal 'x' such that it scares Mr. Smith and doesn't scare Mrs. Smith. It also says that for any other animal 'y' that scares Mr. Smith, if it's not the same as 'x', then it must scare Mrs. Smith.

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