# What is an example of a contrapositive statement?

## What is an example of a contrapositive statement?

For example, consider the statement, “If it is raining, then the grass is wet” to be TRUE. Then you can assume that the contrapositive statement, “If the grass is NOT wet, then it is NOT raining” is also TRUE.

### How do you write a contrapositive statement?

To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement. The contrapositive of “If it rains, then they cancel school” is “If they do not cancel school, then it does not rain.” If p , then q . If q , then p .

#### What is the contrapositive of P → Q?

~q ~p

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.

**What is contrapositive statement in conditional statement?**

Contrapositive Statement The contrapositive of a conditional statement is a combination of the converse and the inverse. The “If” part or p is replaced with the “then” part or q and the “then” part or q is replaced with the “If” part or p. After that, both parts are negated.

**What is the meaning of contrapositive statement in math?**

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”. The contrapositive of a conditional statement is a combination of the converse and inverse.

## What is an example of a conditional statement?

Example. Conditional Statement: “If today is Wednesday, then yesterday was Tuesday.” Hypothesis: “If today is Wednesday” so our conclusion must follow “Then yesterday was Tuesday.” So the converse is found by rearranging the hypothesis and conclusion, as Math Planet accurately states.

### What is a contrapositive in math?

#### Which one is the contrapositive of q → P Mcq?

Explanation: q whenever p contrapositive is ¬q → ¬p.

**What is converse contrapositive and inverse of the statement P → q?**

The converse of the conditional statement is “If Q then P.” 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’s contrapositive mean in math?**

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.

## How do you write the converse inverse and contrapositive of a statement?

We start with the conditional statement “If P then Q.” The converse of the conditional statement is “If Q then P.” 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.”