Definition: Contrapositive is exchanging the hypothesis and conclusion of a conditional statement and negating both hypothesis and conclusion. For example the contrapositive of “if A then B” is “if not-B then not-A”.

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## What is a contrapositive example?

Definition: Contrapositive is exchanging the hypothesis and conclusion of a conditional statement and negating both hypothesis and conclusion. For example the contrapositive of “if A then B” is “if not-B then not-A”.

**What is contrapositive and inverse?**

The contrapositive of the conditional statement is “If not Q then not P.” The inverse of the conditional statement is “If not P then not Q.”

### What is the definition of contrapositive in geometry?

: 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 “

**What is a contrapositive in math?**

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 “

## What is converse proposition?

converse, in logic, the proposition resulting from an interchange of subject and predicate with each other. Thus, the converse of “No man is a pencil” is “No pencil is a man.” In traditional syllogistics, generally only E (universal negative) and I (particular affirmative) propositions yield a valid converse.

**What is a contrapositive in geometry?**

A contrapositive statement occurs when you switch the hypothesis and the conclusion in a statement, and negate both statements. In this example, when we switch the hypothesis and the conclusion, and negate both, the result is: If it is not a polygon, then it is not a triangle.

### What’s contrapositive mean in math?

**What is a contrapositive?**

con·tra·pos·i·tive | \\ ˌkän-trə-ˈpä-zə-tiv , -ˈpäz-tiv\\. : 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 “.

## What is the contrapositive of a conditional statement?

The contrapositive of the conditional statement is “If not Q then not P .” The inverse of the conditional statement is “If not P then not Q .” We will see how these statements work with an example. Suppose we start with the conditional statement “If it rained last night, then the sidewalk is wet.”

**What is contraposition in logic?**

In logic, contraposition is an inference that says that a conditional statement is logically equivalent to its contrapositive.

### Is the contrapositive logically equivalent to its converse?

We say that these two statements are logically equivalent. We also see that a conditional statement is not logically equivalent to its converse and inverse. Since a conditional statement and its contrapositive are logically equivalent, we can use this to our advantage when we are proving mathematical theorems.