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# Converse and Inverse

We will now discuss converse, inverse, and contrapositive statements. These sound hard but are actually quite easy once you memorize what they are.

## Converse

The converse of a statement is simply taking the variables in the statement and switching their place. So taking the following example:

If A then B or A -> B

The converse would be

If B then A or B -> A

I told you it was easy.

## Inverse

The inverse of a statement is taking the negation of each variable so with the last example we would have the original statement of:

If A then B or A -> B

The inverse would be

If ~A then ~B or ~A -> ~B

## Contrapositive

The final one is contrapositive which is taking the negation of all the variables in the converse of the statement. So the example would be:

Our original statement:

If A then B or A -> B

Our Converse

If B then A or B -> A

Finally our contrapositive

If ~B then ~A or ~B -> ~A

## Truth Tables

Now lets take a look at the truth table for all these and weâll see something interesting:

Variable 1Variable 2Original StatementConverseInverseContra Positive
ABA -> B B -> A~A -> ~ B~B -> ~ A
TTTTTT
TFFTTF
FTTFFT
FFTTTT

Notice anything about the corresponding truth tables for each statement? Well if you look closely youâll see that the original statement has the same truths as the contrapositive. Also the converse has the same truth table as the inverse. So if a statement is true then you know that the contrapositive statement is also true. Same goes for converse and inverse statements.