# Math Help - How to Prove this WFF

1. ## How to Prove this WFF

Hi Help To Prove this :

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

I Have tried this out :

$
p \Leftrightarrow q \equiv (p \Rightarrow q) \wedge (q \Rightarrow p)
$

2. Originally Posted by parkhid
Hi Help To Prove this :

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

I Have tried this out :

$
p \Leftrightarrow q \equiv (p \Rightarrow q) \wedge (q \Rightarrow p)
$
$p \Leftrightarrow q$ 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 $p \Leftrightarrow q \equiv (\sim p) \Leftrightarrow (\sim q)$.