# What does Contrapositive of a statement mean?

## What does Contrapositive of a statement mean?

Definition of contrapositive : a proposition or theorem formed by contradicting both the subject and predicate or both the hypothesis and conclusion of a given proposition or theorem and interchanging them “if not-B then not-A ” is the contrapositive of “if A then B “

## Can a false conditional statement have a true Contrapositive?

Truth. If a statement is true, then its contrapositive is true (and vice versa). If a statement is false, then its contrapositive is false (and vice versa).

Is the contrapositive logically equivalent to the conditional?

Contrapositive: The contrapositive of a conditional statement of the form “If p then q” is “If ~q then ~p”. Symbolically, the contrapositive of p q is ~q ~p. A conditional statement is logically equivalent to its contrapositive.

### 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.

### How do you determine if a conditional statement is true or false?

A conditional is considered true when the antecedent and consequent are both true or if the antecedent is false. When the antecedent is false, the truth value of the consequent does not matter; the conditional will always be true.

What is an example of a contrapositive statement?

Mathwords: Contrapositive. Switching the hypothesis and conclusion of a conditional statement and negating both. For example, the contrapositive of “If it is raining then the grass is wet” is “If the grass is not wet then it is not raining.”

#### What implication can you give about contrapositive and inverse statements?

The contrapositive of a conditional statement is functionally equivalent to the original conditional. This is because you can logically conclude that a dry driveway means no rain. This means that if a statement is a true then its contrapositive will also be true….The Inverse, Converse, and Contrapositive.

P Q P→Q
F F T

#### Why is the contrapositive logically equivalent to the original statement?

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.

Is for a conditional statement?

A conditional statement is a statement that can be written in the form “If P then Q,” where P and Q are sentences. For this conditional statement, P is called the hypothesis and Q is called the conclusion. Intuitively, “If P then Q” means that Q must be true whenever P is true….Definition.

P Q P→Q
T T F F T F T F T F T T