Mathematical Proof: Proof by Contradiction and Proof by Contrapositive
A mathematical proof is an argument that convinces other people that something is true. In mathematical logic, "likely to be true" is not good enough. We try to prove things beyond any doubt at all.
In your initial post, address the following:
Compare proof by contradiction and proof by contrapositive and provide an example of one or the other.
Define Proof by contradiction, Whereas proof by contrapositive, Steps for proof by contradiction, Steps for proof by contrapositive, An example of proof by contradiction, An example of proof by contrapositive, Importance of proof of contradiction, Importance of proof of contrapositive, Some limits of proof of contradiction, Some limits of proof of contrapositive, Whereas proof by contrapositive
resource1: https://www(dot)youtube(dot)com/watch?v=utf275mqCrk
resource2: https://www(dot)youtube(dot)com/watch?v=Zm5201Q5qyE&feature=youtu.be
Mathematical Proof
Student Name
Institutional Affiliation
Instructor's Name
Date
Proof by Contradiction and Proof by Contrapositive are two methods used to prove the validity of a statement. These methods involve drawing conclusions based on logical deductions made from given premises. Proof by contradiction is a method of proof in which one assumes that the negation of the conclusion is true and then derives a contradiction from this assumption. This implies that if the original statement was true, then its negation must be false, proving its validity. An example is when one wants to prove, "If x is an integer, then x2 is even." To do so using proof by contradiction, we would assume that 'x2 is not even' or, equivalently, ...