Deduction
Syllogism (‘modus ponens’)
Suppose \(P\) and \(Q\) are statements, that \(P\implies Q\) is true, and that \(P\) is true. Then \(Q\) is true.
Indirect Proof
Suppose that \(P\) and \(Q\) are statements, that \(P\implies Q\) is true, and that \(Q\) is false. Then \(P\) is false.
Elimination
Suppose that \(P\vee Q\) is true, and \(P\) is false. Then \(Q\) is true.