# What is the law of contrapositive example?

## What is the law of contrapositive example?

If B is not true, then A is not true. An example of such a contrapositive is: Proposition: If I live in Annapolis, then I live in Maryland. Contrapositive: If I do not live in Mary- land, then I do not live in Annapolis.

## Is modus tollens the same thing as contrapositive?

Modus tollens takes the form of “If P, then Q. Not Q. Therefore, not P.” It is an application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from P implies Q to the negation of Q implies the negation of P is a valid argument.

Are contrapositive always true?

The contrapositive does always have the same truth value as the conditional. If the conditional is true then the contrapositive is true.

### What is an example of modus tollens?

Latin for “method of denying.” A rule of inference drawn from the combination of modus ponens and the contrapositive….

Modus Ponens Modus Tollens
It is bright and sunny today. I will not wear my sunglasses.
Therefore, I will wear my sunglasses. Therefore, it is not bright and sunny today.

### Is contrapositive a direct proof?

To prove: If x2 is even, then x is even. Although a direct proof can be given, we choose to prove this statement by contraposition. The contrapositive of the above statement is: Having proved the contrapositive, we can then infer that the original statement is true.

How do you find the contrapositive of a statement?

The first step to finding the contrapositive is to reverse the order of the subjects of the ‘if’ and the ‘then’ portions of the statement to get the following statement: If it is a canine, then it is a dog. In math and logic, this is called the converse of the original statement.

## Is there more than one contrapositive in a proposition?

In traditional logic there is more than one contrapositive inferred from each original statement. In regard to the “A” proposition this is circumvented in the symbolism of modern logic by the rule of transposition, or the law of contraposition.

## Is the converse of a conditional equivalent to the contrapositive?

For example, the converse of ‘If P, then not-Q’ is ‘If not-P, then Q.’ Whereasa conditional is logically equivalent to its contrapositive, it is clearly not equivalent to its converse. A conditional and its converse issue entirely different inference tickets.

When is contraposition a valid form of immediate inference?

Notice that contraposition is a valid form of immediate inference only when applied to “A” and “O” propositions. It is not valid for “I” propositions, where the obverse is an “O” proposition which has no converse. The contraposition of the “E” proposition is valid only with limitations ( per accidens ).