How to Prove this WFF

Quote:

Originally Posted by parkhid

Hi Help To Prove this :

$<br /> p \Leftrightarrow q \equiv (\sim p) \Leftrightarrow (\sim q)<br />$

I Have tried this out :

$<br /> p \Leftrightarrow q \equiv (p \Rightarrow q) \wedge (q \Rightarrow p)<br />$

$p \Leftrightarrow q$ means $p \Rightarrow q$ and $q \Rightarrow p$ .

From the contrapositive:

If $p \Rightarrow q$ then $(\sim q) \Rightarrow (\sim p)$ .

If $q \Rightarrow p$ then $\sim p \Rightarrow (\sim q)$ .

Therefore $p \Leftrightarrow q \equiv (\sim p) \Leftrightarrow (\sim q)$ .