PROBLEM SOLVING

• Reasoning is the process of drawing conclusion or inferences through the use of proper justification.
• Inductive Reasoning is the process of reasoning that arrives at a general

  conclusion based on the observation of specific examples.
• An object defined by a premise is called a specimen.
• The generalization is called a conjecture.
• A specimen that negates the conjecture is called a counterexample.
• An inductive argument is said to be strong if it makes a compelling case for its conclusion. It is weak if its conclusion is not well supported by the premises.
• Note that the strength of an argument is not necessarily related with the truth of the conclusion.
• Deductive reasoning is the process of reasoning that arrives at a conclusion based on previously accepted general statements.
• Conclusion is based on general statements whose truth value is known or assumed. The process in deductive reasoning is it first lay down definition of terms, and assume basic true statements called axioms and derive true statements from these axioms called as theorems.
• A deductive argument is said to be valid if its conclusion follows from its

  premises, regardless of the truth of the premises or conclusion.
• A deductive argument is said to be sound if it is valid and its premises are all true.
• In 1945, Hungarian mathematician George P ́olya’s devised a model for

  problem solving and published it in his book How to Solve It. The book

  contains a collection of mathematical and non-mathematical problems with selected strategies on dealing these.
• 1. Understand the problem
  2. Devise a Plan
  3. Carry out the Plan
  4. Look back