Mathematical proofs | Propositional calculus | Methods of proof
In logic, the contrapositive of a conditional statement is formed by negating both terms and reversing the direction of inference. More specifically, the contrapositive of the statement "if A, then B" is "if not B, then not A." A statement and its contrapositive are logically equivalent, in the sense that if the statement is true, then its contrapositive is true and vice versa. In mathematics, proof by contrapositive, or proof by contraposition, is a rule of inference used in proofs, where one infers a conditional statement from its contrapositive. In other words, the conclusion "if A, then B" is inferred by constructing a proof of the claim "if not B, then not A" instead. More often than not, this approach is preferred if the contrapositive is easier to prove than the original conditional statement itself. Logically, the validity of proof by contrapositive can be demonstrated by the use of the following truth table, where it is shown that p → q and q → p share the same truth values in all scenarios: (Wikipedia).
The Contrapositive and Proof by Contrapositive
The contrapositive is a powerful tool that can be used to prove various mathematical statements. It is most useful when a direct proof is awkward or impossible, and - if it can be used - is often a much more elegant method that employing proof by contradiction. #proof #contrapositive #proo
From playlist Proofs and Explanations
Writing the contrapositive statement from a conditional statement
👉 Learn how to find the contrapositive of a statement. The contrapositive of a statement is the switching of the hypothesis and the conclusion of a conditional statement and negating both. If the hypothesis of a statement is represented by p and the conclusion is represented by q, then the
From playlist Contrapositive of a Statement
Proof by Contrapositive: If a + b is odd, then a is odd or b is odd
This video provides an example of proof by contrapositive. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
How to determine the contrapositive of a conditional statement
👉 Learn how to find the contrapositive of a statement. The contrapositive of a statement is the switching of the hypothesis and the conclusion of a conditional statement and negating both. If the hypothesis of a statement is represented by p and the conclusion is represented by q, then the
From playlist Contrapositive of a Statement
Introduction to Proof by Contrapositive: If n squared is even, then n is even
This video introduces the mathematical proof method of proof by contrapositive and provides an example of a proof. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
How to write the contrapositive from a conditional statement
👉 Learn how to find the contrapositive of a statement. The contrapositive of a statement is the switching of the hypothesis and the conclusion of a conditional statement and negating both. If the hypothesis of a statement is represented by p and the conclusion is represented by q, then the
From playlist Contrapositive of a Statement
Learning to write the contrapositive of a conditional statment
👉 Learn how to find the contrapositive of a statement. The contrapositive of a statement is the switching of the hypothesis and the conclusion of a conditional statement and negating both. If the hypothesis of a statement is represented by p and the conclusion is represented by q, then the
From playlist Contrapositive of a Statement
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From playlist The Nature of Proof
Proof Exercise: State the Contrapositive, Converse and Negation, Then Prove the Truth Value
This video explains how to determine the contrapositive, converse, and negation of a statement. Then the truth value is determine and a proof is provided. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
We look at the technique of proof by contrapositive and give several examples. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Website: http://www.michael-penn.net Randolph College Math: http://ww
From playlist Proof Writing
The basic idea of proof by contrapositive + two examples! Comment below with questions, make sure to like / subscribe, and keep flexin' those brain muscles! Facebook: https://www.facebook.com/braingainzofficial Instagram: https://www.instagram.com/braingainzofficial
From playlist Proofs
Proving conditional statements -- Proof Writing 10
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From playlist Proof Writing
Examples of Contrapositive Proofs -- How to do Mathematical Proofs (PART 8)
This is part 8 of a series of videos on: How to do mathematical proofs. The course is structured in such a way to make the transition from applied-style problems in mathematics (sometimes referred to as engineering mathematics) to pure mathematics much smoother. The course will cover the
From playlist How to do Mathematical Proofs
A Brief Introduction to Proofs
This video serves as an introduction to proofs.
From playlist Summer of Math Exposition Youtube Videos
Now that we know what connectives and quantifiers are, we can put that knowledge to use to figure out how to prove when statements of the form "For all x in D, if p(x), then q(x)" are true (or demonstrate that they are false).
From playlist Linear Algebra