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Converse,the contrapositive and the inverse of these condition

annie

New member
Sep 14, 2013
6
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
Jan 27, 2012
196
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
Sep 14, 2013
6
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
Jan 27, 2012
196
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
Sep 14, 2013
6
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
Jan 27, 2012
196
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!

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