lec2 - Math 117 March 31, 2011 2 Proof Inductive reasoning...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 117 – March 31, 2011 2 Proof Inductive reasoning is the type of reasoning in which one draws a conclusion about the general case from considering particular examples. Deductive reasoning is the type of reasoning in which one draws a conclusion by applying a general principle to a particular case. Inductive reasoning by itself does not constitute a proof. One needs to use a deductive argument to prove the conclusion, even if the conclusion was first obtained by inductive reasoning. Most theorems can be formulated in the form p q , in which case p is called the hypothesis and q is called the conclusion . When constructing a proof of the implication p q , one usually builds a logical bridge of simpler implications: p p 1 p 2 ··· ⇒ ··· ⇒ q 2 q 1 q. The contrapositive of p q is q ⇒∼ p , and it is equivalent to the original implication, i.e. ( p
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.
Ask a homework question - tutors are online