Mathematical logic | Theorems in propositional logic
In logic and mathematics, contraposition refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as proof by contraposition. The contrapositive of a statement has its antecedent and consequent inverted and flipped. Conditional statement . In formulas: the contrapositive of is . If P, Then Q. — If not Q, Then not P. "If it is raining, then I wear my coat" — "If I don't wear my coat, then it isn't raining." The law of contraposition says that a conditional statement is true if, and only if, its contrapositive is true. The contrapositive can be compared with three other statements: Inversion (the inverse), "If it is not raining, then I don't wear my coat." Unlike the contrapositive, the inverse's truth value is not at all dependent on whether or not the original proposition was true, as evidenced here.Conversion (the converse), "If I wear my coat, then it is raining." The converse is actually the contrapositive of the inverse, and so always has the same truth value as the inverse (which as stated earlier does not always share the same truth value as that of the original proposition).Negation (the logical complement), "It is not the case that if it is raining then I wear my coat.", or equivalently, "Sometimes, when it is raining, I don't wear my coat. " If the negation is true, then the original proposition (and by extension the contrapositive) is false. Note that if is true and one is given that is false (i.e., ), then it can logically be concluded that must be also false (i.e., ). This is often called the law of contrapositive, or the modus tollens rule of inference. (Wikipedia).
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
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
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
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
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
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From playlist The Nature of Proof
What are the different types of conditional statements
👉 Learn how to find the inverse, the converse, and 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 conclusio
From playlist Converse, Inverse, Contrapositive Conditional Statements
What are the different forms of conditional statements
👉 Learn how to find the inverse, the converse, and 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 conclusio
From playlist Converse, Inverse, Contrapositive Conditional Statements
Write the conditional, converse, inverse, and contrapositive of the statement ex
👉 Learn how to find the inverse, the converse, and 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 conclusio
From playlist Converse, Inverse, Contrapositive Conditional Statements
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
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)
Converse, Inverse, & Contrapositive - Conditional & Biconditional Statements, Logic, Geometry
This geometry video tutorial explains how to write the converse, inverse, and contrapositive of a conditional statement - if p, then q. This video also discusses the definition of a biconditional statement. It contains plenty of examples and practice problems. The converse is simply the
From playlist Geometry Video Playlist
Converse and Contrapositive Example (Chinese Food and Milk)
This video provides and example of a converse and contrapositive of a given implications.
From playlist Mathematical Statements (Discrete Math)
Contrapositive Statements - Logic
This video focuses on how to write the contrapositive of a conditional statement. In particular, this video shows students how to flip and negate a conditional statement. Furthermore, the concepts of truth value and logical equivalence is discussed. Your feedback and requests are encourag
From playlist Geometry
What are examples of a statements converse, inverse, and contrapositive
👉 Learn how to find the inverse, the converse, and 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 conclusio
From playlist Converse, Inverse, Contrapositive Conditional Statements