Week 6 Methods of proof

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soru English cevap English
Waht is a proof?
öğrenmeye başla
proving that a statement is true or flase
What is an argumennt?
öğrenmeye başla
is a finite collection of statementsp1, p2,..., pn called premises (or hypotheses) followed by a statement q called the conclusion
Waht is a premis?
öğrenmeye başla
the section of an argument containing declarative statments
what is a hypothesis?
öğrenmeye başla
the section of an argument containing declarative statements
what is a conclusion?
öğrenmeye başla
the section of an argument giving the final statment
what is a valid argument?
öğrenmeye başla
when the premis supports the conclusion in all cases
what is a direct proof?
öğrenmeye başla
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?
öğrenmeye başla
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?
öğrenmeye başla
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?
öğrenmeye başla
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?
öğrenmeye başla
an example that disproves a statement or proposition

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