##### Propositional Logic

## Converse and Contrapositive

### Subjects to be Learned

- converse of proposition
- contrapositive of proposition

### Contents

For the proposition P Q, the proposition
Q P is called its **converse**,
and the proposition Q
P is called its **contrapositive**.
For example for the proposition "If it rains, then I get wet",

**Converse**: If I get wet, then it rains.

**Contrapositive**: If I don't get wet, then it does not rain.

The converse of a proposition is not necessarily logically equivalent to it, that is
they may or may not take the same truth value at the same time.

On the other hand, **the contrapositive of a proposition is always
logically equivalent to the proposition**. That is, they take the same truth value regardless
of the values of their constituent variables.
Therefore, "If it rains, then I get wet." and "If I don't get wet,
then it does not rain." are logically equivalent. If one is true then the other is also true, and vice versa.

### Test Your Understanding of Converse and Contrapositive

**Indicate which of the following converses and contrapositives are correct and which are not.
**

**Click Yes or No , then Submit. There are two sets of questions.**

**
Next -- Variation of if_then **

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