Inverse, Converse, Inverse

[Guest]

I understand converse and inverse. I wil attempt to show you that I do. However I
am not sure of this problem. Please help! Here is the problem:

What is the inverse of the converse of the inverse of the conditional statement "if p, the q"?

This is what I have.
conditional statement is P => q
converse q=>p
inverse of converse ~q => ~P
my answer is q => p, which is the converse

Please help!!!!!

 

[galactus]

The converse of \(\displaystyle {p\to{q}}\) is \(\displaystyle {q\to{p}}\)

The contrapositive of \(\displaystyle {p\to{q}}\) is \(\displaystyle \sim{q}\to\sim{p}\)

Is inverse the contrapositive?.

 

[Guest]

Is that the inverse of the converse of the inverse

I agree the contrapositive is the inverse of the converse. But is it the inverse of the
converse of the inverse of p then q???

 

[pka]

It appears you got the correct answer but in the wrong order.
\(\displaystyle \begin{array}{ll}
p \to q & \mbox{statement}\\
\sim p \to \sim q & \mbox{inverse of statement} \\
\sim q \to \sim p & \mbox{converse of inverse of statement}\\
q \to p & \mbox{inverse of converse of inverse of statement}\\
\end{array}\)

 

[Guest]

OKay, got it

Thanks, for your help! So I had it right!!!! WOW