Truth tables are designed to show all the possible truth values that a statement, or a collection of statements, can have. It is necessary to find the truth values for a collection of statements because that is what an argument is–a collection of statements. But to construct a truth table for a single statement, it is necessary to set out an array of possible truth values for each and every simple statement that makes up the entire complex statement. And for arguments, the same procedure is followed.
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