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You make a statement that is either a true one or a false one. Simple as that. For example, you might say "The moon is made of green cheese" as a false statement and most people know that's wrong.
They made be crude or sophisticated
A Proof, 2-column proofs for geometry are common.
A synonym for false is fake, made-up, fictitious and pretend. incorrect, wrong, mistaken, misleading, faulty, inaccurate, invalid, erroneous
He made an indisputable statement about global warming, or so he thought...