# Converse,the contrapositive and the inverse of these condition

#### annie

##### New member
q)give the converse ,the contrapositive and inverse of these conditional statements
a)if it rains today,then i will drive to work
b)if |x|=x then x>=0
c)if n is greater than 3,then n^2 is greater then 9

#### Plato

##### Well-known member
MHB Math Helper
Re: converse,the contrapositive and the inverse of these condition

q)give the converse ,the contrapositive and inverse of these conditional statements
a)if it rains today,then i will drive to work
b)if |x|=x then x>=0
c)if n is greater than 3,then n^2 is greater then 9
If P then Q. What are the converse ,the contrapositive and inverse of that statement?

#### annie

##### New member
Re: converse,the contrapositive and the inverse of these condition

If P then Q. What are the converse ,the contrapositive and inverse of that statement?
converse q then p
contrapositive not q then not p
inverse not p then not p
i dont understand how to do b part

#### Plato

##### Well-known member
MHB Math Helper
Re: converse,the contrapositive and the inverse of these condition

converse q then p
contrapositive not q then not p
inverse not p then not q
i dont understand how to do b part
b) $$\displaystyle \text{If }|x|=x\text{ then }x\ge 0~.$$

Inverse: $$\displaystyle \text{If }|x|\ne x\text{ then }x< 0~.$$

Now you post the others.

#### annie

##### New member
Re: converse,the contrapositive and the inverse of these condition

b) $$\displaystyle \text{If }|x|=x\text{ then }x\ge 0~.$$

Inverse: $$\displaystyle \text{If }|x|\ne x\text{ then }x< 0~.$$

Now you post the others.
converse if x>=0 then |x|=x
contrapositive if x ne 0 then |x| ne x

#### Plato

##### Well-known member
MHB Math Helper
Re: converse,the contrapositive and the inverse of these condition

converse if x>=0 then |x|=x
contrapositive if x ne 0 then |x| ne x
NO!

$$\displaystyle \text{If }x<0\text{ then }|x|\ne x~.$$