What Is a True Statement in Logic?
Technically speaking, there are no true or false statements in logic, only valid or invalid arguments. An argument is valid if it would be true whether the statements that make it up are true or false.
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Logical Statements
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Logical statements are composed of individual propositions, combined with logical operators such as "and," "or," "if/then," "implies" and "not." For example, "'If P then Q' implies 'If Q then P'" is a logical argument.
Validity of Logical Arguments
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The validity of a logical argument can be evaluated via a truth table. In a truth table we list each combination of the components of the argument being true or false. If, as in our example, there are two components (P and Q) then there are four combinations: Both true, both false, P true Q false and Q true P false. If the result is true regardless the combination, the argument is valid; otherwise, it is invalid.
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Truth Tables
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The truth table for our example argument is as follows:
If P and Q are both true, then both "If P then Q" and "If Q then P" are true, and so is the full statement, which becomes "If true then true", which is true.
If P is true and Q is false, then "If P then Q" is false, and if "Q then P" is true, and the whole statement becomes "if false then true," which is true.
If both P and Q are false, then both "If P then Q" and if "Q then P" are true, and so is the full statement, which becomes if "false then false."
But if P is false and Q is true, then "If P then Q" is true and "If Q then P" is false and the whole statement becomes "If true then false," which is false.
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