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September 12, 2023

Which of the Following is Not a True Statement?

If I ask you which of the following is not a true statement, what do you think it will mean?

The question is not formulated correctly, because there is no such thing as a "true statement" that can be proven to be either true or false. The true statement is a proposition, which is a declarative sentence that makes an assertion about reality. The false statement is a contradiction, which is an utterly unfalsifiable statement. If you were to ask the question, "Is the Mona Lisa a beautiful work of art?" it would be impossible to answer that question, as the answer is purely subjective and personal opinion rather than factual information.

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Definitions of terms:

A necessary condition: a compound statement consisting of the form "p if and only if q" (ex. This ball will fall from the window if it is dropped from the window); a necessary condition is true if the truth value of all its premises is the same and false otherwise.

A sufficient condition: a compound statement consisting of two or more statements joined by the form "p or q" (ex. Mary has blue hair and Tom has purple hair); a sufficient condition is true if the truth values of all its conjuncts are the same and false if not.