believes that Al Gore was President of the USA on April 20, 2000, but she does not believe that the moon is made of green cheese, then the sentence

:"Mary believes that Al Gore was President of the USA on April 20, 2000"

is true while

:"Mary believes that the moon is made of green cheese"

is false. In both cases, each component sentence (i.e. "Al Gore was president of the USA on April 20, 2000" and "the moon is made of green cheese") is false, but each compound sentence formed by prefixing the phrase "Mary believes

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