PROOFS IN MATHEMATICS
WHAT IS A PROOF ? Proof of a mathematical statement consists of sequence of statements, each statement being justified with a definition or an axiom or a preposition that is previously established by the method of deduction using only the allowed logical rules. Thus each proof is a chain of deductive arguments each of which has its premises and conclusions . Many a times, we prove a preposition directly from what is given in the preposition. But some times it is easier to prove an equivalent preposition rather than proving the preposition itself. This leads to, two ways of proving a preposition directly or indirectly and the proofs obtained are called direct proofs and indirect proof and further each has three different ways of proving which is discussed below. Direct proof Straight forward proof: It is a chain of arguments which leads directly from what is given or assumed, with the help of axioms, definitions or already proved theorems, to what is to be proved using r