0
$\begingroup$

How can I simplify this: $(\neg p \rightarrow p)= p$?

I already tried every rule I know, but I can't find the correct result.

$\endgroup$

3 Answers 3

3
$\begingroup$

Using $p\rightarrow q= \lnot p\lor q$, you have $\lnot p \rightarrow p = p \lor p = p$.

$\endgroup$
1
$\begingroup$

If $p$ is true, then $\lnot p\rightarrow p$ is also true, because "false implies true" is true.

If $p$ is false, then $\lnot p\rightarrow p$ is also false, because "true implies false" is false.

So $p$ and $\lnot p\rightarrow p$ are logically equivalent.

$\endgroup$
0
$\begingroup$

You just need to check that both expressions agree for all values of $p$.

If $p=T$, then L.H.S. = $(F \rightarrow T)=T=p$.

If $p=F$, then L.H.S. = $(T \rightarrow F)=F=p$.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .