An Introduction to Formal Logic

Summary of logical notions

• An argument is (deductively) valid if it is impossible for the premises to be true and the conclusion false; it is invalid otherwise. 
• A tautology is a sentence that must be true, as a matter of logic. 
• A contradiction is a sentence that must be false, as a matter of logic. 
• A contingent sentence is neither a tautology nor a contradiction. 
• Two sentences are logically equivalent if they necessarily have the same truth value. 
• A set of sentences is consistent if it is logically possible for all the members of the set to be true at the same time; it is inconsistent otherwise.