# How to Prove this WFF

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• February 27th 2010, 04:54 AM
parkhid
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)
$
• February 27th 2010, 05:02 AM
Prove It
Quote:

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