 A proof is a statement which arises as a result of true statements. The last statement is called the conclusion and each statement before it are called the premise or hypotheses or assumption.
 The rules of inference are
 Law of detachment (or Modus Ponens):
p  q  p→q  p→q∧p 
T  T  T  T 
T  F  F  F 
F  T  T  F 
F  F  T  F 
 Law of contraposition or Modus Tollens: p→q∧∼q
 Different methods of proof:
 Direct proof: A proof of p⇒q begins with the assumption that p is true and with the repeated use of laws of detachment proves that q is true.
 Indirect proof: ∼p⇒∼q i.e.(p⇒q)≡(∼p→∼q)
 Counterexamples: A counterexample to a statement p proves that p is false i.e. ∼p is true.
