Week 6 Methods of proof

Waht is a proof?

proving that a statement is true or flase

What is an argumennt?

is a finite collection of statementsp1, p2,..., pn called premises (or hypotheses) followed by a statement q called the conclusion

Waht is a premis?

the section of an argument containing declarative statments

what is a hypothesis?

the section of an argument containing declarative statements

what is a conclusion?

the section of an argument giving the final statment

what is a valid argument?

when the premis supports the conclusion in all cases

what is a direct proof?

we start with the hypothesis of a statement(premises) and make one deduction after another until we reach the conclusion

what is proof by contradiction?

if supposing that the premises are true and the conclusion is false we are able to arrive at a contradiction(a conclusion that is contradictory to our assumptions or something obviously untrue like 1=0)=>our conclusion must be true!

what is proof by contrapositive?

to prove a statement by contrapositive, we prove the contrapositive statement by a direct proof and conclude that the original statement is true

What is mathematical induction?

Let P be a predicate that is defined for integers n. Suppose Basis stepP(a)is true for some particular integer a; Inductive step For all integers k>=a, if P(k)is true, then P(k+1)is true. Then P(n)is true for all integers n>=a

what is a counter example?

an example that disproves a statement or proposition