# Week 6 Methods of proof

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Question

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

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